Ebola Optimization Search Algorithm: A New Nature-Inspired Metaheuristic Optimization Algorithm

Nature computing has evolved with exciting performance to solve complex real-world combinatorial optimization problems. These problems span across engineering, medical sciences, and sciences generally. The Ebola virus has a propagation strategy that allows individuals in a population to move among susceptible, infected, quarantined, hospitalized, recovered, and dead sub-population groups. Motivated by the effectiveness of this strategy of propagation of the disease, a new bio-inspired and population-based optimization algorithm is proposed. This study presents a novel metaheuristic algorithm named Ebola Optimization Search Algorithm (EOSA) based on the propagation mechanism of the Ebola virus disease. First, we designed an improved SIR model of the disease, namely SEIR-HVQD: Susceptible (S), Exposed (E), Infected (I), Recovered (R), Hospitalized (H), Vaccinated (V), Quarantine (Q), and Death or Dead (D). Secondly, we represented the new model using a mathematical model based on a system of first-order differential equations. A combination of the propagation and mathematical models was adapted for developing the new metaheuristic algorithm. To evaluate the performance and capability of the proposed method in comparison with other optimization methods, two sets of benchmark functions consisting of forty-seven (47) classical and thirty (30) constrained IEEE-CEC benchmark functions were investigated. The results indicate that the performance of the proposed algorithm is competitive with other state-of-the-art optimization methods based on scalability, convergence, and sensitivity analyses. Extensive simulation results show that the EOSA outperforms popular metaheuristic algorithms such as the Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), and Artificial Bee Colony Algorithm (ABC). Also, the algorithm was applied to address the complex problem of selecting the best combination of convolutional neural network (CNN) hyperparameters in the image classification of digital mammography. Results obtained showed the optimized CNN architecture successfully detected breast cancer from digital images at an accuracy of 96.0%. The source code of EOSA is publicly available at https://github.com/NathanielOy/EOSA_Metaheuristic.


I. INTRODUCTION
Ebola virus represents the virus causing the Ebola virus disease (EVD).The disease was first so named in the Democratic Republic of the Congo (DRC) in 1976.A widespread catastrophic outbreak was reported in late 2013 in the West African The associate editor coordinating the review of this manuscript and approving it for publication was Zhenzhou Tang .regions, including Sierra Leone, Liberia, Mali, Nigeria, and Senegal.It is widely reported that the virus made its entry into the human population through consumption or contact with infected animals such as fruit bats [1]- [3].This animalto-human infection led to person-to-person infection, becoming an epidemic across the West African region.
Contrary to the novel corona virus (COVID- 19), the EVD person-to-person transmission occurs only when the infected person exhibits some form of signs and symptoms associated with Ebola.This transmission is aided by contact with any form of body fluid of an infected person.A healthy person comes in contact with infected objects since the Ebola virus can survive on dry surfaces such as doorknobs and countertops for several hours [4], [5].The hemorrhagic disease, known to be notoriously fatal, has been reported to have mortality rates ranging from 25% to 90%, with an average of 50% mainly due to fluid loss rather than blood loss [6], [7].Although the experimental Ebola vaccine proved highly protective against EVD, the transmission rate from the infected to the susceptible population is alarming.The high survival rate of EBOV in body fluids, including breast milk, saliva, urine, semen, cerebrospinal fluid, aqueous humor, blood, blood derivatives, and detected in amniotic fluid, tears, skin swabs, and stool by reverse transcription (RT)-PCR, presents a very high infection and transmission rate.This implies that a onetime virus entry into a susceptible population through a single individual has a high propagation rate.
A close study of the propagation strategy of the EVD and the resulting propagation model inspired the metaheuristic algorithm proposed in this study.Deriving computational solutions from natural phenomena has promoted a field of computing referred to as nature-inspired computing.A broader view of this aspect of computing may well relate to the field of Artificial Intelligence (AI) and Computational Intelligence (CI), where computational systems are designed by synthesizing behaviors of organisms or natural phenomena [8]- [10].Metaheuristic algorithms are nature-inspired optimization solutions with high performance.They often require low computing capacity, which has successfully solved complex real-life problems in engineering, medical sciences, and sciences, especially in areas concerning swarm intelligence based algorithms [11]- [20].These optimization algorithms are designed without specific reference to a particular problem.They are often categorized by performing a local or global search, handling single-solutions or whole populations, using memory, and adopting a greedy or iterative search process.The techniques often achieve near-optimal solutions to large-scale optimization problems due to their highly flexible manner of operation and ability to learn quickly owing to their natural or biological systems from which their designs were inspired.
A subfield of natural computation consists of biologyinspired techniques, also referred to as bio-inspired algorithms or computational biology.These techniques are stochastic, far from the design of deterministic heuristics.This feature has made it possible to represent the biological evolution of nature, hence capable of being used as a global optimization solution.Recently, bio-inspired optimization algorithms have helped support machine learning to address the optimal solutions to complex problems in science and engineering [21].The bio-inspired algorithms combine biological concepts with mathematics and computer sciences and are classified as Evolutionary Algorithms (EA), Biology, and Swarm Intelligence (SI).Although the last two categories are often combined and referred to as swarm intelligence, not all bio-inspired algorithms have the swarm feature.Examples of evolutionary algorithms are Genetic Algorithms (GA) [22], Genetic Programming (GP), Differential Evolution (DE), the Evolution Strategy (ES), Coral Reefs Optimization Algorithm (CRO) [23], and Evolutionary Programming (EP).Examples of SI-based algorithms are: food foraging behavior of honeybees Artificial Bee Colony (ABC) [24], [25], echolocation ability Ant-lion Optimizer (ALO), luciferin induced glowing behavior Bees Algorithm (BAO), Bat Algorithm (BOA) [26], hunting behavior Barnacles Mating Optimizer (BMO), swarming around hive by honey bees Cuckoo Optimization Algorithm (COA), echocancellation Cuckoo Search Optimization (CSO) [27], hunting behavior and social hierarchy Dolphin Echolocation Optimization (DEO), social interaction and food foraging Dragonfly algorithm (DFA), Static and dynamic swarming behavior Deer Hunting Optimization (DHO), Pollination process of flowers Fire-fly Algorithm (FFA), Food foraging behavior Hunting search (FFO), bubble-net hunting Fruit Fly Optimization Algorithm (FOA), obligate brood parasitic behavior Flower-Pollination Algorithm (FPA), navigation and foraging behaviors Grasshopper Optimization Algorithm (GOA), spiral flying path of moth Glowworm Swarm Optimization (GSO), cuckoos' survival efforts Grey Wolf Optimizer (GWO) [28], flashing light patterns Moth-Flame Optimization (MFO), Mating behavior Manta Ray Foraging Optimizer (MRFO), Hunting behavior of humans SailFish optimizer (SFO), Group hunting behavior Salp Swarm Algorithm (SSA), and Hunting mechanism of Whale Optimization Algorithm (WOA) [29].Others are Blue Monkey Optimization (BMO) [30], Arithmetic Optimization Algorithm (AOA) [31]- [33], Aquila Optimizer (AO) [34], Reptile Search Algorithm (RSA) [35], and Sandpiper Optimization Algorithm (SOA) [36].
These EA and SI-based algorithms have demonstrated good performance in solving real-world complex combinatorial problems, which are considered a fundamentally vital and critical task.In addition, studies have shown their capability to efficiently scale up to handle large-scale problems as opposed to traditional optimization methods, which are more effective for small-scale problems [37].Further research in bio-inspired computing areas will lead to achieving similar and better new optimization algorithms capable of solving modern-day optimization problems.Our study showed that exploring the propagation model of diseases with endemic and pandemic natures may yield an outperforming optimization algorithm with interesting performance in solving real-world optimization problems.This study considered that optimization algorithms' exploration and exploitation phases are practically coupled into the natural order and strategy of propagation of these diseases.Studies confirm that finding a good balance between exploitation and exploration of the problem search space for an optimization algorithm determines its ability to find a globally optimal solution [38], [39].The exploration phase often allows for finding candidate solutions that are not neighbor to the current solution, while exploitation maintains its search in the neighborhood.Hence, we found a balance of the two scenarios in the disease propagation model for escape from a local optimum without neglecting good solutions in the neighborhood.
In this study, we propose a novel metaheuristic algorithm referred to as the Ebola Optimization Search Algorithm (EOSA), inspired by the Ebola virus disease and its propagation model (a preprint has previously been published [40]).We derived the novel algorithm through a careful study of our implementation of the SIR model of the disease.Particularly, our algorithm's novelty brought into metaheuristic design lies in the mechanism to balance between the exploration and exploitation phases.Secondly, the algorithm demonstrates an inherent ability to use a dynamic mechanism to update solutions as they transit through susceptible profitably, infection, quarantine, recovered, and hospitalized compartments.Initialization of solutions in the population follows the natural pattern of the disease through the application of a stochastic model.To quantitatively measure how fit a given solution is in solving the problem, give intuitive results, and discover the best or worst candidate solution, the resulting optimization algorithm is investigated on about forty-seven (47) classical benchmark optimization functions [41] and more than thirty (30) CEC functions [42].In summary, the main contributions of this research are as follows: i.An improved SIR model of Ebola disease and a modified mathematical model is designed to aid the proposed algorithm.ii.We design a new nature-inspired metaheuristic algorithm using the models in (i).iii.Applied EOSA to optimize the hyperparameters of a CNN architecture to image classification problem detecting breast cancer.iv.Several experiments are conducted using over 89 mathematical optimization problems, including the classical benchmark functions and IEEE-CEC test suite, which are considered challenging test problems in the literature to evaluate the efficiency of the proposed EOSA.v. Validation of the obtained numerical results using statistical analysis test further supports the superiority claim of the proposed EOSA optimization method over the existing state-of-the-art metaheuristic algorithms.The rest of the paper is organized as follows.Section 2 provides an overview of the Ebola virus diseases.The proposed propagation model, mathematical model, and algorithmic design for the EOSA algorithm are given in Section 3. Section 4 details the benchmark functions applied to evaluate the performance of the proposed algorithm.Also, this section lists and discusses the parameterization and assignment of initial values used for experimentation.A discussion on results obtained is presented in Section 5, including numerical simulations that support the proposed propagation model.A detailed comparative analysis of the performance of EOSA and similar algorithms is also presented in the section.In Section 6, we give concluding remarks on how our novel optimization algorithm fits in the literature, its real-life applicability, and perspectives for future works.

II. RELATED WORK
This section summarises the Ebola virus disease, its propagation technique, and relevant SIR-based models that support this study.Also, considering the nature of the optimization algorithm proposed in this study which shares some principles of biology, we review studies that have developed bioinspired optimization algorithms.

A. THE EBOLA VIRUS (EBOV) AND EBOLA VIRUS DISEASES (EVD): THE PROPAGATION MECHANISM
Ebola viruses result in what is known as the Ebola virus disease (EVD) once they successfully infect the host, suggesting victimization of the host.They are classified among the family of Filoviridae viruses, which are recognized by their different shapes of short or elongated branched filaments sizing up to 14,000 nanometers in length [6].About six different species of the EBOV have been reported to exist.Bundibugyo Ebola virus, Ebola-Zaire virus, Tai Forest Ebola virus, and Sudan Ebola virus account for large flare-ups or outbreaks in Africa.
Exposure of a human individual to the virus through pathogenic agents or a contaminated environment initiates a population-based infection and after that, propels the spread of the disease.Direct contact with infected individuals spurs the propagation and spread of the virus.This contact relies on broken skin or mucous membranes in the eyes, nose, mouth, or other openings.It is assumed that such openings in the human body allow for body fluids (e.g.urine, saliva, sweat, faeces, vomit, breast milk, amniotic fluid, blood, and semen) bearing the virus to be transmitted to other susceptible individuals.Another host to the Ebola virus, which may transmit the disease to a healthy or susceptible individual, is a contaminated environment.An environment, such as medical equipment, clothes, bedding, and other related utensils, is considered contaminated if the body fluid of an infected individual has been spilt within or upon such an environment or object.Whereas an infected individual and a contaminated environment appear to have enhanced the propagation of EVD, infected animals consumed by humans have also been shown to propagate the disease [43].These animals include bats, chimpanzees, fruit bats, and forest antelope, often hunted for food.Another propagative mechanism of the EBOV is culturally driven by burial practices in most affected populations and regions, with transmission occurring through contact with infected dead bodies.Meanwhile, note that the Ebola virus is not propagated through the air.
The application of different strategies, including casebased management approach, surveillance and contact tracing, quarantine of infected cases, infection prevention and control practices, and safe burial rites, has been adopted to revive and survive infected cases.However, infected cases remain positive while the virus remains in their blood.The infection and propagation rate of the EBOV presents an appealing computational solution to numerous problems and so motivates the design of the proposed metaheuristic algorithm.While it appears that the solutions for mitigating the spread of the virus are suggestive of scaling down the infection rate, we argue that some other factors are still contributory to the propagation model.For instance, it is widely reported that the time-scale from symptom onset to death is an average of 10 days in 50-90% of cases [44].
To formalize and apply the propagation model of EBOV, we review some susceptible-infection-recovery (SIR) models.This is necessary for mainstreaming the concept proposed in the study.An interesting SIR model, based on EBOV, combining agent-based and compartmental models, has been presented [5].The authors suggested that the hybrid model can switch from one paradigm to another on a stochastic threshold.The agent-based model consists of Susceptible (S), Infected (I), Hospitalized (H), Recovered (R), Funeral (F), and Dead (D).The Exposed (E) item was added to make up seven (7) compartments in the compartmental model.The SIR-based model was proposed to model the movement of individuals in a population from one compartment to another in both paradigms.For instance, individuals may move from Susceptible (S), Infected (I), to Hospitalized (H), based on a pre-existing computed rate.One external compartment considered in the literature is the influence of EBOV-carrying animals like bats.The assumption made was that since these animals can infect the human population without them (the animals) becoming ill, they present a reservoir-like mechanism for the virus in the SIR model.
Furthermore, the authors assumed that the rate of infection and hospitalization between infected individuals who will recover or die is the same, the deceased individual is buried in unsafe practices, and that recovered individuals are removed from the system.This SIR model presents a foundation for the modeling and implementation of the optimization algorithm proposed in this study.We considered that the compartments defined by Tanade et al. (year) work demonstrate the possibility to monitor and simulate the propagation model of the EBOV for the optimization task in our study.
In related work, Berge et al. (year) also modeled the propagation model of EBOV using the SIR-type model.The novelty of the study was the addition of the role of the indirect environmental transmission on the dynamics of EVD and to assess the effect of such a feature on the long run of the disease [45].The authors showed that factoring direct and indirect transmission of EBOV into an SIR model promotes a system where the virus always exists in a population, increasing the propagation rate.Taking a cue from the novelty of this work in addition to that of Tanade et al. (year), we adapted the model proposed in this study to support the concept of direct and indirect transmission promoted by Berge et al. (year).Both studies supported their SIR models with mathematical models and further simulation to validate the performance of their model.
Similarly, Yet [46] successfully represented the basic interactions between EBOV and wild-type Vero cells in vitro .
Rafiq et al. (year) also proposed the SEIR model, which mathematical model supported demonstrating the dynamics and illustrating the stability pattern of the Ebola virus in the human population.Their mathematical model is in the form of a couple of linear differential equations.The authors applied their SEIR model to study the disease-free equilibrium (DFE) and endemic equilibrium (EE) to report the stability of the model.Another study investigating the spread of EVD in India is [47] hoping to find EBOV transmission in the region through an SEIR model.Using ordinary differential equations, the study represented the SEIR model as a mathematical model and simulated it using a spatiotemporal epidemiology modeler (STEM).Rachah and Torres [47] also applied a mathematical model to study the outbreak of EBOV and eventually the EVD.The novelty of this study is the addition of vaccination to the proposed model.We found this appealing considering the role of the vaccine in stemming the tide of the infected population.Whereas most SEIR approaches have often adopted the stochastic method for the simulation of the model, Okyere et al. [48] considered using a deterministic scheme for designing models and studying the infection rate of EBOV.As an improvement to the work of Rachah and Torres (year), which factored in vaccination, the study also captured treatment and educational campaigns as time-dependent control functions in the SEIR model proposed.
This study developed a comprehensive SEIR-based model with more compartments, considering the above review.The proposed SEIR model factored in the notion of quarantine, which we found to play a role in curtailing EBOV propagation.In addition, we modeled the SEIR model to allow for the inclusion of the influence of vaccines in the pace of the growth of infection among a given population.The SEIR model was then formulated using an ordinary differential equation.This presented a good understanding of the design of the proposed metaheuristic algorithm.The resulting model is detailed in Section 3 and its supporting mathematical model.

B. METAHEURISTIC OPTIMIZATION ALGORITHMS: BIOINSPIRED-BASED ALGORITHMS
Bio-inspired optimization algorithms represent a class of metaheuristic algorithms whose principles are inspired by biology and natural phenomena.Generally, these algorithms have successfully been applied to solve different optimization problems in engineering and other related fields [49].This category of algorithms exploits the basic processes of nature and then translates them into rules or procedures, which are then modeled computationally for solving complex real-life problems [50]- [57].They are mostly populationbased algorithms, and examples of such are Satin Bowerbird Optimizer (SBO), Earthworm Optimisation Algorithm (EOA), Wildebeest Herd Optimization (WHO), Virus Colony Search (VCS), Slime Mould Algorithm (SMA), Invasive Weed Colonization Optimization (IWO), Biogeography-Based Optimization (BBO), Coronavirus Optimization Algorithm (COA), Emperor Penguin Salp Swarm Algorithm (ESA).Although evolutionary-based algorithms like GA and DE and swarm-based algorithms like PSO, WOA, and ABC share some characteristics of a biology-inspired algorithm, we have chosen to limit our review to those listed.
ESA is a hybrid of two phenomena drawn from the Salp Swarm Algorithm and Emperor Penguin.The behaviour of the two creatures is modelled to achieve ESA.Comparing the proposed algorithm with similar metaheuristic algorithms, authors [58] revealed that the algorithm demonstrated good performance based on sensitivity, scalability, and convergence analyses.Coronavirus Optimization Algorithm (COA) based on its propagation strategy, and another variant, namely Coronavirus Herd Immunity Optimizer (CHIO) based on human immunity, has been proposed.The COA proposed in [59] and CHIO in [60] leveraged infection and herd immunity.The effectiveness of COA was evaluated by applying it to the design of the convolutional neural network (CNN) problem, while CHIO proved robust at real-world engineering problems.Earthworm Optimisation Algorithm (EOA), also referred to as EWA, is a metaheuristic algorithm whose inspiration was drawn from the reproductive nature of the earthworm [61].The mechanism involves two reproduction strategies where the first strategy allows for a parent to reproduce only one offspring while the other allows for more than one offspring.This reproducibility is controlled by the Cauchy mutation approach allowing for crossover operators.
Biogeography-Based Optimization (BBO) solves its optimization problem by implementing the geographical distribution and positioning of biological organisms [62].Alluding to the fact that BBO's features are similar to those of GAs, the authors drew inspiration from the original mathematical model of the biogeography of organisms to derive BBO.Experimentation shows that BBO successfully solved realworld sensor selection problems to detect the status of aircraft engines and a selection of 14 benchmark optimization functions.Invasive Weed Optimization (IWO) is an optimization algorithm that has been widely applied to numerous problems and is based on numerical stochastic optimization algorithms learnt from the invasive nature of weeds [63].The aggressive invasive nature of weeds allows for colonizing the environment against other economically viable plants.Knowing that this is a disadvantage agricultural-wise, the concept has benefited from solving optimization problems.The resulting algorithm was successfully applied to engineering problems, namely optimization and tuning the robust controller and well-known benchmark functions.Satin Bowerbird Optimization (SBO) is a biology-based optimization algorithm whose inspiration was drawn from the phenomenon of the male satin bowerbird's capability of attracting the female for breeding.[64].The Satin Bowerbird Optimizer (SBO) algorithm has been successfully applied to the optimization problem in estimating the efforts needed to develop software.Wildebeest Herd Optimization (WHO) is a bio-inspired metaheuristic algorithm rooted in the behavior of wildebeest when searching for food [65].A lookout for grazing land often guides the search with a high vegetation density.The WHO exploits the following natural characteristics of herds of wildebeest to achieve its performance: local search capability of wildebeest due to limited eyesight, look out for sparsely grazed region to avoid crowded grazing, exploitation of past experiences to explore regions with a high density of vegetation, starvation avoidance strategy deployed through the transition to new regions or location, and lastly, herdbased movement to avoid predators.
The propagation strategy of the virus in the host environment can sometimes be aggressive and often overwhelm the whole environment.Authors [39] proposed Virus Colony Search (VCS) motivated by this mechanism.The VCS exploration and exploitation phases leverage the propagation approach of the virus through diffusion or infection of the host environment.VCS has been successfully applied to the classic benchmark functions and the modern CEC2014 benchmark functions and real-life problems regarding energy consumption management [66].Slime Mould Algorithm (SMA) optimization algorithm is based on a fungus named slime mould, which inhabits cold and humid places [67].The algorithm's authors explored the nutritional stage, also referred to as plasmodium of the organism, for its design.They have a mechanism for multiple food sources and at the same time form a connected venous network so that they can even grow to more than 900 square centimeters depending on food availability.Using a mathematical model, the authors were able to simulate the process of producing positive and negative feedback of the propagation wave of slime mould based on bio-oscillator to form the optimal path for connecting food with excellent exploratory ability and exploitation propensity.SMA was successfully applied to solve engineering problems, including cantilever, welded beam, and pressure vessel structure problems.
While we acknowledge that these are not exhaustive and many new optimization algorithms inspired by natural processes are being developed, they provide the reader with a general understanding of the inspiration and principle behind such a class of algorithms.

III. METHODOLOGY: EOSA METAHEURISTIC ALGORITHM
Understanding how an SEIR-based model works in the propagation of a disease is important to appealing for the design of an optimization algorithm.Hence, this section presents an improved SEIR model based on recent literature on EVD.Secondly, a presentation of the procedural flow of EOSA and the corresponding flow chart are presented and discussed.Lastly, to formalize the proposed optimization algorithm, we represent the SEIR model using a mathematical model and then the algorithm.

A. SIR MODEL OF EOSA
SEIR-based models designed for EVD have been proposed in the literature to monitor both direct and indirect propagation of the disease in the affected population [45] and [5].This study adopts and adapts two relevant models from the existing SEIR models by identifying and adding new compartments perceived as omitted.These compartments are the contaminated environment serving as a reservoir of the virus, vaccination and quarantine, denoted by PE, V, and Q, respectively.This became necessary considering that the Ebola virus and disease are not propagated among the human population except by an individual infected from the reservoir.Also, the roles played by vaccination and quarantined infected individuals have impacted on the propagation rate of the virus.This perception is supported by recent studies [68]- [71].This therefore necessitated the re-modeling of the propagation model which now yielded the SEIR-HDFVQ: Susceptible (S), Exposed (E), Infected (I), Recovered (R), Hospitalized (H), Death or dead (D), Funeral (F), Vaccinated (V), and Quarantine (Q).Also, in designing the model, we considered that an insignificant number of recovered cases might still retain the virus in their body fluid, which has potency for infecting healthy individuals [72]- [74].Since this study's interest was to leverage the propagation model of the EVD for developing an optimization algorithm, it became necessary to explore all factors supporting increased infection.The model of the SEIR-HDVQ is shown in Figure 1, and the listing of its parameters is presented in Table 1.The propagation of EVD is assumed to provide a suitable manner for solving some optimization problems considering its aggressive infection rate is overwhelming communities.The  recover without hospitalization.An assumption made in this study was classifying every vaccinated case as hospitalized.Also, we assumed that both the hospitalized (H) and nonhospitalized cases could transit into the dead (D).At the same time, those recovered (R) from vaccination (V) are returned to the susceptible (S).
The rates of change of variables or parameters applied in this study are summarized in Table 1.The values of most of these parameters are already predetermined by related studies on EVD and are detailed in Section 4. The flowchart presents the flow of process and information as a buildup from the procedure described above.The detailing shows the various levels of initialization and conditional checking.Also, the computation leading to the exploration and exploitation stages of the proposed EOSA metaheuristic algorithm are demonstrated.Lastly, the procedure for updating all subgroups is identified.In the following subsection, the algorithm's mathematical model, as it applies to the flowchart, is presented and discussed.

C. MATHEMATICAL MODEL OF EOSA
To update the positions of each exposed individual, Equation (1) applies: where ρ represents the scale factor of displacement of an individual, mI t+1 i and mI t i are the updated and original positions respectively at time t and t + 1. M (I ) is the movement rate made by individuals and is defined thus: (2) The exploitation stage is designed based on the assumption that the infected individual either stays within a distance of zero (0), or is displaced within a limit not exceeding sratewhere srate denotes short distance movement.The exploration phase is founded on the fact that the infected individual moves beyond the average neighborhood range lrate.The consideration in this study is that the farther the displacement, the more the number of individuals in S are exposed to infection.Both cases are shown in Equations ( 2) and (3).The srate and lrate are regulated by a neighborhood parameter such that when neighborhood is >= 0.5, an individual has moved beyond the neighborhood leading to the mega infection; otherwise it remains within the neighborhood, which curbs infection.

1) INITIALIZATION OF SUSCEPTIBLE POPULATION
At the beginning, an initial population is generated by random number distribution whose initial positions are all zero (0).The individual is generated as shown in Equation ( 4).The U i and L i denote the upper and lower bounds respectively for the i th individual, where I ranges from 1,2,3. . .N, in the population size.
The selection of the current best is computed on the set of infected individuals in time t as seen in Equation ( 5 Update of Susceptible (S), Infected (I), Hospitalized (H), Exposed (E), Vaccinated (V), Recovered (R), Funeral (F), Quarantine (Q), and a system of ordinary differential equations govern dead (D) based on those in [45] and [5].Differential calculus is a branch of calculus that is a branch in mathematics.The former deals with the rate of change of one quantity concerning another, while the latter deals with finding different properties of integrals and derivatives.In our case, the application of differential calculus intends to obtain the rates of change of quantities S, I, H, R, V, D, and Q with respect to time t.Hence, the Equations ( 6)-( 12) are as follows: We assume that Equations (6)(7)(8)(9)(10)(11) are scalar functions, meaning that each has one number as a value, which can be represented as a float.This is not far removed from some common scalar differential equations and their corresponding f functions, such as exponential growth of money or populations governed by scalar differential equations: u = αu, where u is the growth rate.
We determine the rate of change of the population of susceptible individuals and then apply it to the current size of the susceptible vector to obtain the number of susceptible individuals at time t.The same procedure is applied to compute the set of individuals in vectors I, H, R, V, D, and Q using rates described in Table 1.This study assumes the  11) is for the burial rate.Equation ( 12) models the rate of quarantine of infected cases of Ebola.

D. ALGORITHM DESIGN OF EOSA
The pseudo-code of the proposed EOSA metaheuristic algorithm is shown in Algorithm 1. Lines 1-7 of the algorithm show the initialization phase.To naturalize the concept that not all infected cases have the potency for recruiting newly infected individuals, on Line 8 we show that some I are drawn into quarantine status so that the remaining fraction of I infect S population.On Lines 10-24, new infections are generated from S and then added to I. Since R, V, H, and V are only derivable from I, Lines 25-29 of Algorithm 1 generate individuals using corresponding equations of subgroups.Logically, recovered and dead cases need to be removed from I before the next iteration.In our demonstration, recovered cases are added back to S while dead individuals are replaced in S with new cases -to promote the idea of new births as shown on Lines 29-31.Finally, the best solution is computed, and the termination criterion is checked so that when satisfied, the algorithm terminates, otherwise return to Line 7. To demonstrate the usability of the algorithm, we follow on in the next section for experimental setup, configurations, and parameter definition.

IV. EXPERIMENTAL SETUP
This section presents the computational environment applied for experimentation.First, we show the control parameter settings and variable assignment, then a listing of the benchmark functions applied to the algorithm, and finally detail the evaluation criteria.

A. CONFIGURATION OF THE EXPERIMENTAL SETUP
Exhaustive experimentation evaluated the proposed EOSA in a workstation environment with the following configurations: Intel (R) Core i5-7500 CPU 3.40GHz, 3.41GHz; RAM of 16 GB 64-bit Windows 10 OS for each configuration of the system on the network.A total of ten (10) existing metaheuristic algorithms were implemented and experimented with for comparative purposes with the EOSA algorithm.This study executed each algorithm twenty (20) times to ensure fairness in each algorithm's evaluation.Also, five hundred (500) epochs were covered in each run.The runs of 20 for each algorithm allowed computing the average values for all metrics.

B. PARAMETERS OF EOSA METAHEURISTIC ALGORITHM
The design and selection of EOSA's parameters and corresponding values assumed the natural definitions generated from those reported in the literature.In this study, we adopted the rates reported in studies that have extensively evaluated the SEIR models.These studies relied on the WHO data for the evaluation of their models.All these parameters have been described in Section 3, where the SEIR-HDVQ model was presented.
In Table 2, the initial value for each parameter is defined.Considering the stochastic nature of EOSA, which is characteristic of biology-based optimization algorithms, values for some parameters are randomly assigned.The problem size applied for all experimentation is fixed at one hundred (100).We note that these values remain fixed for all experiments on the benchmark functions.

C. BENCHMARK FUNCTIONS
To evaluate the effectiveness of the proposed EOSA metaheuristic algorithm, this study applied forty-seven (47) standard and high dimensional functions for this purpose.These functions are listed in Table 3 and are subsequently used for performance comparison with similar metaheuristic algorithms.We listed the names, mathematical representation, and range of the functions.We also evaluated the algorithm using the IEEE-CEC benchmark functions to demonstrate exhaustive experimentation.
Whereas many test functions are continuous, they are categorized into four (4).Test functions characterized by unimodal, convex, and multidimensional forms are first class.They represent a class of test functions with interesting functions with cases capable of slowing down convergence or even yielding a poor convergence.The resulting convergence trails from such a slow pace to a single global extremum.The second class consists of test functions of type multimodal, two-dimensional with few local extremes.This test function category appeals to situations where we intend to test the quality of standard optimization procedures in an anticipated hostile environment.This hostile environment describes problem domains with only a few local extremes with a single global one.The third and fourth classes represent a list of test functions known as multimodal twodimensional with a huge number of local extremes, and multimodal multidimensional, with a huge number of local extremes.It has been shown that these test functions work well for situations where the quality of intelligent and resistant optimization algorithms are tested [41], [75]- [79].

D. EVALUATION METHOD
The following metrics were considered in the performance evaluation: mean, median, standard deviation, maximum values, minimum or worst values, average values, overall convergence time, and average execution time.In addition to these, we applied the outcome of the proposed EOSA and related optimization algorithms to statistical tests to evaluate their performance in terms of convergence to determine algorithms capable of generating similar final solutions.

V. RESULT AND DISCUSSION
A detailed performance evaluation of the outcome of the experimentation carried out in Section 4 is presented and discussed in this Section.First, we study the performance of the proposed SEIR-HDVQ model to determine how it effectively describes the natural phenomenon.Performance evaluation uses the values obtained from applying the optimization algorithms to the test functions.Compared with other methods, the proposed algorithm's performance is statistically analysed.Also, the application of the algorithm to medical image classification using convolutional neural network (CNN) architectures is presented.

A. SIMULATION OF EVD PROPAGATION BASED ON SEIR-HDVQ MODEL
The simulation of the proposed SEIR-HDVQ model applied to EOSA during experimentation is demonstrated.The result is reported to investigate the naturalization tendency of the SEIR-HDVQ model as obtained in the real-life propagation model for the EVD and EBOV.
In Figure 3, the curves for Susceptible (S), Infected (I), Recovered (R), Hospitalized (H), Dead (D), Vaccinated (V), and Quarantine (Q) are captured so that they show the rate at which each compartment rises and falls within a period of fifty (50) epochs.In the Figure, we observed that the early phase of the infection outbreak rose against the susceptible population.The Figure also revealed the response to the rising infection rate through quarantine measures, such that as infection rose, the number of quarantine individuals also increased -a measure to stem the outbreak.Meanwhile, we noticed that recovery and death rate curves wobbled along with infection and quarantine.
Table 4 lists the outcome for the best, worst, mean, median, and standard deviation for each of the 47 functions.An overview of the results showed that although EOSA outperformed most of the algorithms in most cases for the 47 functions, some interesting differences were noticed, which appears to group the outcome into two.Whereas EOSA demonstrated a very close performance compared to ABC, WOA, BOA and PSO, we observed that EOSA's outcome compared with DE, GA, and HGSO was significantly better.For example, for F1-4, F6-7, F12, F14-15, F18, F20-23, F2, F29-30, F32-36, F38, F40-43, and F46-47, EOSA clearly achieved the best values in all cases.However, in the cases of F5, F9-11, F13, F16-17, F19, and F25-26, EOSA was outperformed based on WOA and BOA, ABC, WOA, and PSO, ABC, BOA and PSO, ABC and PSO, ABC, ABC, WOA, and BOA, respectively.Meanwhile, we found some situations for the 47 functions where there was no clear superiority of EOSA over similar algorithms, neither were the similar algorithms able to demonstrate clear superiority.These cases are found in F28, F31, F37, F39, F44, and F45, where we observed that ABC and PSO beat EOSA, beaten by WOA, BOA and PSO, ABC, matched values in ABC and PSO, beaten by WOA, and beaten by ABC, WOA, and PSO respectively As shown in Table 4 for the 47 functions, the values obtained for the worst revealed a strong competition between EOSA and ABC, WOA, BOA, and PSO.We discovered that only in the cases of F3, F6, F12, F18, F22-23, F27, F29, F28, and F40-41 were the values of EOSA better than those listed earlier and also completely outperformed those same algorithms in the cases of F13, F21, F25, and F32.However, we noticed that the discrepancies reported by these algorithms compared to EOSA were not significantly large.Meanwhile, DE, GA, and HGSO maintained a significant variation in the values obtained for best and worst computations.This implied that the proposed EOSA algorithm and its competitive related algorithms (ABC, WOA, BOA, and PSO) performed significantly well over DE and GA.Meanwhile, we found the performance of SOA and HGSO very competitive with that of EOSA.For instance, when investigating the overall superiority of each algorithm compared with others, the following were observed: EOSA (12), ABC(4), WOA(1), BOA(1), PSO(1), DE(1), GA(2), BMO(0), HGSO (19), and SOA (21).This shows that both HGSO and SOA had more occurrences of superiority.Interestingly, when each method was compared with EOSA, the following were observed: ABC/EOSA(15/28), WOA/EOSA(5/28), BOA/EOSA(2/28), PSO/EOSA(4/28), DE/EOSA(0/28), GA/EOSA(0/28), BMO/EOSA(0/28), HGSO/EOSA(23/21), and SOA/EOSA (22/20).
We note that although other similar metaheuristics algorithms may compete with the EOSA method on the sets of the various mathematical benchmark functions tested in this study, it is noteworthy that the comparison with the selected algorithms showed that the performance of EOSA is very competitive.
To confirm the outstanding performance and superiority of the EOSA, the convergence curves of the history of solutions are graphed in Figure 4.The benchmark functions F1, F2, F3, F4, F7, F8, F20, F25, F26, F27, F43, and F45.We observed that in all cases, the curve of the plots descended appreciably.The implication is that the EOSA algorithm is a very competitive optimization algorithm that can discover optimum solutions in exploration and exploitation operations.To demonstrate the superiority of EOSA, when its convergence curve was plotted against those of state-of-the-art algorithms, we found that its solutions were significant.
The convergence of EOSA using the benchmark functions as compared with ABC, WOA, PSO, and GA was graphed and is illustrated in Figure 5.The Figures showed that in most cases, the best values for all the algorithms were descending from their initial peak values to a lower value as the training improved over some epochs.The graphing was achieved by obtaining the best values for each case of EOSA, ABC, WOA, PSO, and GA at 1, 50, 100, 200, 300, 400, 500 iteration points.The Figure confirms that the best values for GA are often larger than the others except in a few cases where ABC also has some large values.However, ABC, WOA, PSO, and the proposed EOSA do not just have low values for the best cases but appear to only drop in value for small fractions across all the iterations.This is why their rise and fall concerning their curves was not so pronounced compared to that of GA and sometimes ABC.
Perspective views of some selected functions, alongside the search history, are shown in Figures 6 and 7. Again,   to compare the performance of EOSA with other similar optimization algorithms, the illustrations in the Figures were graphed with all the selected algorithms.The outcome for F1function showed that EOSA appeared to converge its points more closely compared with ABC while WOA showed only a point.However, in the cases of F3 and F34, PSO and GA converged their point more closely than EOSA.Meanwhile, as in the case of the F1 function, we found that EOSA converged its points more closely than BOA and ABC.
In Figure 6a, we show the search history of the proposed EOSA algorithm at the initial iteration.This allows for a comparison of the initial solutions with the final solutions, which is shown in Figure 6b.
The second illustration is shown in Figure 6b.Only in the cases of F7 and F28 was GA able to cluster its points more closely than EOSA, PSO, BOA, DE, and ABC.While PSO attempts to achieve a clearer cluster in F28, EOSA also performs well in clustering points or solutions in F7, F28, F45, and F46.

C. EVALUATION OF EOSA ON CONSTRAINED CEC BENCHMARK FUNCTIONS
The result of experimentation with constrained functions of CEC was also collected and is reported in this subsection.The CEC functions consist of fourteen ( 14) functions, and we further experimented with thirty (30) hybrids of the 14 CEC functions.The derivation for the hybrid functions is listed in Table 5. C1-C8 and C10 are shifted (S) versions of their corresponding CEC functions, while C9 and C11-C16 are shiftrotate (SR) versions of their corresponding CEC functions.Functions C17-C22 represent shift versions of a combination of some CEC functions, while those of C23-C30 are hybrids of predefined CEC hybrids.The total number of CEC-based functions used for the experiments is forty-four (44).
In Figure 8, the curves of the convergence of EOSA on the solutions of CEC benchmark functions are shown.We graphed the outcome of the optimized solutions over 1, 50, 100, 200, 300, 400 and 500 epochs.To demonstrate this, we plotted the curves of CEC_F1-14 and C_F1.The outcome of the pattern of the curves showed that the solutions were well optimized over the epochs.The convergence of the EOSA algorithm based on the best fit compared with the best fits of ABC, WOA, BOA, PSO, DE, GA, and HGSO we plotted as shown in Figure 9.All the curves representing each optimization algorithm showed a descent from high to low based on their best values.Although the curves of ABC and occasionally that of GA were often seen overshooting in values compared with others, we confirm that this is unrelated to the significantly large values obtained by these algorithms (ABC and GA, with DE and HGSO inclusive).EOSA, WOA, BOA, and PSO curves appear to lie low, though with marginal descent continuously overshadowed by ABC and GA.

D. COMPUTATIONAL TIME COST FOR EOSA AND RELATED ALGORITHMS ON BENCHMARK AND CEC FUNCTIONS
The computational time required for running the optimization algorithms discussed in previous subsections was recorded and reported.We took an average of the computation time for all the forty-seven (47) standard benchmark functions and the forty-four (44) CEC-based functions.The outcome of these averages for ABC, WOA, BOA, PSO, DE, GA, and HGSO compared to EOSA are listed in Table 11.We discovered that the computational requirement of EOSA reports a minimal CPU time compared with other algorithms.
The computational requirement for executing all the algorithms on the standard benchmark functions was graphed as shown in Figure 10.We randomly selected some of these functions: F1, F2, F3, F4, F5, F7, F8, F14, F20, F27, F33, F37, F17, F26, D45, and F44.Although EOSA consumed the lowest CPU time in all cases, we noticed that the discrepancies in the case of F27, F33, F2, and F14 were quite marginal.On the other hand, EOSA's computational requirements in the case of F1, F4, and F8 were significantly low compared with related optimization algorithms.
Similarly, in Figure 11, the computational requirement for CEC-based functions was illustrated for some selected functions namely CEC01, CEC02, CEC03, CEC04, CEC05, CEC06, CEC07, CEC10, CEC11, CEC12, C1, C9, C25, and C30.In all cases, the CPU time for training EOSA was lower than other related algorithms.While EOSA showed less CPU time, GA and ABC were more demanding for this same computational resource.We note that the unusual computational time accounted for in some of the algorithms might  not be unconnected with occasions when several algorithms experimented on the same system.

E. COMPARING THE PERFORMANCE OF EOSA WITH SIMILAR METHODS USING STATISTICAL TEST
Using the results obtained from the forty-seven (47) standard benchmark functions, we validated the performance gain of EOSA against those of ABC, WOA, BOA, PSO, DE, GA, and HGSO using statistical analysis.The Friedman mean rank test was carried out to achieve this, and the result obtained is shown in Table 12.The results showed that the proposed EOSA method ranked best above all other methods by yielding a mean rank of 1.60.The PSO, WOA, and BOA trail after it while HGSO, GA, ABC, and DE follow in that order.
The test statistics (χ 2 ) result for the Friedman test revealed an overall statistically significant difference between the mean ranks of the eight (8) methods, namely: EOSA, ABC,    WOA, BOA, PSO, GA, DE and HGSO.The test statistics (χ 2 ) value of 249.847380 was obtained along with degrees of freedom (df) of 7 and significance level (Asymptotic Significance) of 0.001.We discovered a statistically significant difference in performance of the eight (8) methods compared based on the values of χ 2 (7) = 249.847380,p = 0.001.The existence of this significant difference then necessitated the need for a Wilcoxon signed-rank test.Each of the methods (optimization algorithm) was uniquely combined with EOSA to determine where the significance lay.Running the test, the results in Table 13 show   In summary, based on the outcome of the exhaustive experimentation done in this study, EOSA has shown to be a search algorithm capable of finding better solutions in a tight competition with state-of-the-art optimization algorithms.Also, the proposed algorithm demonstrated that it can find far better solutions with fewer computational requirements when compared with ABC, WOA, BOA, PSO, GA, DE, and HGSO methods.

F. APPLICATION TO MEDICAL IMAGE CLASSIFICATION PROBLEM
In this section, we present the performance of the proposed EOSA algorithm in addressing the complex problem of selecting the optimal combination of hyperparameters of convolutional neural (CNN) architecture.The resulting optimized CNN architecture is then applied to feature detection and classification of digital mammographic images to characterize breast cancer abnormalities.The architecture of the CNN model applied to this task is shown in Figure 12.
Table 14 shows a comparative analysis of the performance for hybridization of CNN and three optimization algorithms CNN-GA, CNN-WOA, and CNN-EOSA.We applied the GA, WOA and EOSA optimization algorithms to optimize the hyperparameters of the CNN architecture.The optimization algorithms and the resulting optimized CNN architecture were trained for five (5) epochs and compared performance.Meanwhile, the traditional CNN architecture with no optimization applied to it was also trained for the same number of epochs.Results obtained showed that the un-optimized CNN architecture showed the least accuracy compared with an optimized version of the same architecture.Comparing the accuracies of CNN-GA, CNN-WOA, and CNN-EOSA, we found that CNN-EOSA demonstrated superior performance.Also, we captured the loss values obtained for all the variations of the CNN architecture, as shown in the table listing.Furthermore, the trained models obtained from training CNN, CNN-GA, CNN-WOA, and CNN-EOSA were applied to test data, and performance was also compared using the metrics: accuracy, precision, recall, and F1 score.The prediction achieved using the trained model is listed in Table 15.The result again confirmed that optimizing the hyperparameters of CNN architecture using a metaheuristic algorithm is essential.However, more interesting is the performance comparison of the application of the algorithm to optimize the traditional CNN architecture.We observed that the hybrid of CNN-EOSA outperformed CNN-GA and CNN-WOA when comparison was made using the metrics mentioned earlier.This further confirms the EOSA algorithm's applicability to effectively address the problem of medical image classification with particular mention to breast cancer classification from digital mammography samples.
In addition to the classification problem of breast cancer, we also investigated the performance of the EOSA-CNN algorithm on the lung cancer dataset.The experimental results obtained are outlined in Table 16, where the accuracy, Cohens Kappa, specificity, sensitivity, precision, recall, F1-score and balanced accuracy are computed and reported.CNN-EOSA algorithm outperforms the other hybrid models and the traditional CNN in most of the metrics used for the evaluation.Again, this confirms that CNN-EOSA successfully detected the features of each class and correctly classified them in an excellent performance accuracy rating.For instance, the best values obtained for accuracy for CNN-GA, CNN-WOA, and CNN-EOSA are 0.81, 0.81, and 0.82, respectively.We see that in all these tests, the CNN-EOSA algorithm yielded a better performance when compared with other hybrid algorithms.In addition to the CNN-EOSA surpassing other hybrids, we also noticed that it outperformed the basic CNN architecture by an increase of 0.06.
Figure 13 shows the confusion matrix plot for all hybrid algorithms with respect to all the class labels observed in the dataset.The classification accuracy of all classes is indicated for each plot of the confusion matrix to give an accurate report on their performances.Taking the case of CNN-EOSA as an example, we see that 90% of all cases with normal label were correctly identified and over 86% of cases labelled as malignant were correctly identified by the proposed hybrid algorithm.
The performance of the EOSA metaheuristic algorithm on the standard benchmark functions, IEEE-CEC constraint function, and its application to the challenge of image classification in the detection of breast cancer are all strong, unbiased indicators of the viability of the newly proposed metaheuristics algorithm.

VI. CONCLUSION
This paper has presented a novel optimization algorithm, EOSA, based on the propagation model of the deadly Ebola virus and its associated disease.The study has shown how the bio-inspired algorithm derived its efficiency from the dynamic mechanism of moving individuals in the population through the susceptible, infected, quarantined, hospitalized, recovered, and dead sub-populations.The study presented an improved version of the propagation model of the Ebola virus disease, which was further translated into a mathematical model.The resulting model was applied to the design of the novel EOSA metaheuristic algorithm.We applied EOSA to two sets of benchmark functions consisting of fortyseven (47) classical and over thirty (30) constrained IEEE CEC-benchmark functions.The outcome of extensive experimentation to determine the algorithm's performance showed that it provides performance on a par with other populationbased methods.This performance is seen as competitive with other state-of-the-art related methods from the literature.Although the EOSA metaheuristic algorithm did not show superior performance in all cases, a significant outcome confirms it is very potent in handling optimization problems.
Moreover, considering the no-free lunch theorem, we safely conclude that the optimization fits into the body of recognized and viable optimization algorithms in the literature.A more interesting outcome of the proposed algorithm is the computational demand required for its performance.The experimentation showed that the CPU time for the completion of the algorithm was substantially lower than some state-of-the-art optimization algorithms.Also, we applied the resulting algorithm to the real-world problem of classification of abnormalities in medical (mammography) images to detect breast cancer.EOSA was used to optimize the selection process of obtaining the best combination of hyperparameters of CNN architectures used for the image classification problem.Performance comparison of CNN-EOSA with other similar hybrids confirms the EOSA method's effective applicability.As future work, this study intends to investigate different strategies capable of maximizing a more excellent balance between the exploration and exploitation phase of the algorithm.Also, the constraint of the new algorithm might be overcome using a hybridization solution with other optimization algorithms, demonstrating characteristics of eliminating the constraint.
Figure assumes a population of susceptible individuals whose exposure could trigger the population of other subgroups.Exposed individuals, contaminated environments, and agent reservoirs can randomly draw arbitrary individuals from the susceptible into the category of infected, which may be due to exposure to any individual from the subgroups of the infected.Subgroups of infected individuals are infected from the dead individual, infected individual, recovered individual, contaminated environment, and agent-reservoir.We show that the virus has the potential of decaying in its contaminated environment.Furthermore, the propagation model shows that the infected cases could die without going to a hospital and

B. FLOWCHART OF EOSA 1 .
Motivated by the performance of the SEIR-HDVQ model, we derived the design of the EOSA algorithm.The formalization of the EOSA algorithm is achieved from the following procedure: Initialize all vector and scalar quantities which are individuals and parameters: Susceptible (S), Infected (I), Recovered (R), Dead (D), Vaccinated (V), Hospitalized (H), and Quarantine (Q). 2. Randomly generate the index case (I 1 ) from susceptible individuals.3. Set the index case as the global best and current best, and compute the fitness value of the index case.4. While the number of iterations is not exhausted and there exists at least an infected individual, then a.Each susceptible individual generates and updates their position based on their displacement.Note that the further an infected case is displaced, the more the number of infections, so that short displacement describes exploitation, otherwise exploration.i. Generate newly infected individuals (nI) based on (a).ii.Add the newly generated cases to I. b.Compute the number of individuals to be added to H, D, R, B, V, and Q using their respective rates based on the size of I. c. Update S and I based on nI.d.Select the current best from I and compare it with the global best.e.If the condition for termination is not satisfied, go back to step 6. 5.Return global best solution and all solutions.In Figure 2 below, the flow chart of the proposed EOSA metaheuristic algorithm is shown.

FIGURE 3 .
FIGURE 3.An estimated propagation curve of the Ebola virus and disease based on the simulation with randomly generated data while experimenting with the EOSA optimization algorithm.The curve illustrates variations in the values of Susceptible (S), Infected (I), Recovered (R), Hospitalized (H), Dead (D), Vaccinated (V), and Quarantine (Q) using the SEIR-HDVQ model.

TABLE 4 .
Comparison of best, worst, mean, median and standard deviation values for ABC, WOA, BOA PSO, EOSA, DE, GA, HGSO, SOA, and BMO metaheuristic algorithms using the classical benchmark functions over 500 runs and 100 population size.TABLE 4. (Continued.)Comparison of best, worst, mean, median and standard deviation values for ABC, WOA, BOA PSO, EOSA, DE, GA, HGSO, SOA, and BMO metaheuristic algorithms using the classical benchmark functions over 500 runs and 100 population size.TABLE 4. (Continued.)Comparison of best, worst, mean, median and standard deviation values for ABC, WOA, BOA PSO, EOSA, DE, GA, HGSO, SOA, and BMO metaheuristic algorithms using the classical benchmark functions over 500 runs and 100 population size.TABLE 4. (Continued.)Comparison of best, worst, mean, median and standard deviation values for ABC, WOA, BOA PSO, EOSA, DE, GA, HGSO, SOA, and BMO metaheuristic algorithms using the classical benchmark functions over 500 runs and 100 population size.

FIGURE 5 .
FIGURE 5. Convergent curves of EOSA and related optimization algorithms in some selected standard benchmark functions.

FIGURE 6 .
FIGURE 6. a.A perspective view of the search history for functions F1, F3, F32, and F34 for EOSA optimization algorithm at the initial iteration.b.A 3D and 2D perspective view for functions F1, F3, F32, and F34 t their corresponding search history for EOSA and related optimization algorithms.

FIGURE 7 .TABLE 5 .
FIGURE 7. A 3D and 2D perspective view for functions F7, F28, F45, and F46 and their corresponding search history for EOSA and related optimization algorithms.

FIGURE 9 .
FIGURE 9. Convergent curves of EOSA and related optimization algorithms on some selected CEC functions.

FIGURE 10 .
FIGURE 10.A graphical illustration of computational time required for the execution of EOSA compared with ABC, WOA, PSO, and GA for the standard benchmark functions.

FIGURE 11 .
FIGURE 11.A graphical illustration of computational time required for the execution of EOSA compared with ABC, WOA, PSO, and GA for the CEC functions.

FIGURE 13 .
FIGURE 13.An illustration for confusion matrix for CNN-GA, CNN-WOA and CNN_EOSA hybrid algorithms.

TABLE 1 .
Notations and description for variables and parameters for SEIR-HDVQ.

gBest and
): cBest all denote the best solution, global best solution, and current best solution at time t; fitness represents the objective function applied to the problem.We distinguish gBest and cBest as infected individuals who are Superspreader and Spreader of the Ebola virus, respectively.

TABLE 2 .
Notations and description of variables and parameters for SEIR-HDVQ.

TABLE 6 .
Comparison of best values for EOSA with ABC, WOA, BOA PSO, DE, GA, and HGSO metaheuristic algorithms using the CEC functions over 20 runs and 100 population size.

TABLE 7 .
Comparison of mean values for EOSA with ABC, WOA, BOA PSO, DE, GA, and HGSO metaheuristic algorithms using the CEC functions over 20 runs and 100 population size.

TABLE 8 .
Comparison of standard deviation values for EOSA with ABC, WOA, BOA PSO, DE, GA, and HGSO metaheuristic algorithms using the CEC functions over 20 runs and 100 population size.Mean values for EOSA, ABC, WOA, BOA, and PSO demonstrated a very close outcome with no clear leading

TABLE 9 .
Comparison of worst values for EOSA with ABC, WOA, BOA PSO, DE, GA, and HGSO metaheuristic algorithms using the CEC functions over 20 runs and 100 population size.

TABLE 10 .
Comparison of median values for EOSA with ABC, WOA, BOA PSO, DE, GA, and HGSO metaheuristic algorithms using the CEC functions over 20 runs and 100 population size.

TABLE 12 .
Friedman mean ranks test for EOSA compared with similar optimization algorithms.

TABLE 13 .
Wilcoxon Post hoc test of EOSA with each of the selected optimization methods.

TABLE 14 .
Performance comparison of CNN, CNN-GA, CNN-WOA, and CNN-EOSA in terms of accuracy and loss.

TABLE 15 .
Comparison of performance of CNN, CNN-GA, CNN-WOA and CNN-EOSA in terms of classification accuracy, precision, recall, and F1 score.

TABLE 16 .
The overall and per class performance of the CNN-GA, CNN-WOA, and CNN-EOSA hybrid algorithms and as compared with the basic CNN architecture.