Bio-Inspired Ant Lion Optimizer for a Constrained Petroleum Product Scheduling

Real-world optimization problems demand sophisticated algorithms. Over the years bio-inspired approach, a subset of computational intelligence has demonstrated remarkable success in real-world use cases, especially where exact or deterministic algorithms are ineffective. Petroleum product scheduling is a complex optimization task belonging to the combinatorial problem category. The problem size and the constraints compound the complexity of the petroleum product scheduling problem. However, conventional optimization methods such as the exact or deterministic algorithm produced a poor solution quality to the petroleum products scheduling problem. Therefore, this study leverages the potency of a bio-inspired approach, Ant Lion Optimizer (ALO) in its basic state to enhance the solution quality. This is in line with She-Shin Yang’s proposition, father of bio-inspired algorithms who advocated for the application of existing bio-inspired algorithms to tackle real-world problems rather than developing new algorithms. Bio-inspired is a computational paradigm that models the characteristics of natural biological entities to solve complex problems. We also used the Chaotic Particle Swarm Optimization (CPSO) algorithm for the same problem to unveil the efficacy of the roulette wheel function in ALO. The results show a 24.8% and 23.9% reduction in the original cost of distribution on ALO and CPSO respectively. Also, 99.5% of the constraints are met. Thus, problems of scarcity, minimum allocation and product availability are solved using the penalty constraint handling method. The exact algorithm showed a 14% reduction in the original cost. However, despite the effectiveness, further work on constraint handling methods and other bio-inspired computation approaches such as Genetic algorithms and their variants could be possible in the future scope. Moreover, other real-world problem domains such as power distribution in the power, sector could be a possible application of the ALO.


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Optimization is an all-domain-centric subject. It involves 24 searching for the best alternative given an objective function 25 subject to constrained or unconstrained variables [1]. Amidst 26 several options, finding the best solution could be complex or 27 nearly impossible. Optimization need arises when there are 28 unlimited resources. To this end, every organization strives 29 The associate editor coordinating the review of this manuscript and approving it for publication was Christian Pilato .
to strategically plan and design their system to maximize 30 profit amidst scarce resources [2]. Conventional optimization 31 techniques may not give optimum solutions to some problems 32 as demonstrated in this study [3]. The problem complexity 33 suggests the need for a more sophisticated optimization tech- 34 nique. The problem size and the constraints are the major 35 characteristics of a complex problem, and many real-world 36 problems belong to this category. Typically, scheduling is 37 a combinatorial optimization problem. Combinatorial opti-38 mization is finding an optimal solution to perform a collection 39 networks [21], [22], [23]. A variety of constrained handling 96 methods is integrated into the algorithm to obtain an optimum 97 or near optimum solution. Such constrain handling meth-98 ods like the penalty method, separatist approach, feasibility 99 preserving technique [24], and Lagrange multiplier [25]. 100 Petroleum product optimization is a complex task; thus, 101 it belongs to the class of combinatorial problems [26]. 102 From the preceding, it could be deduced that gradient-based 103 algorithms are used in the petroleum optimization model 104 evaluation. Studies have shown that the gradient-based opti-105 mization method is not effective in solving some real-world 106 problems [27]. Among the limitations of the conventional 107 gradient-based methods are poor solution quality, high 108 computation cost, and implementation complexity [28]. 109 Bio-inspired algorithms have shown better alternatives to 110 conventional methods [29], [30], [31], [32]. Upon this 111 premise, therefore, the study models and evaluates petroleum 112 product scheduling optimization using a subsection of a pub-113 lic refinery in Nigeria. The bio-inspired algorithm approach 114 would be employed to implement the model and compare the 115 result using the existing conventional method in the literature. 116 The remaining parts of the paper are structured as fol-117 lows: Section II discusses the related concepts and works; 118 Section III presents the study methodology while Section IV 119 presents the results. The study's final remark and future scope 120 are presented in Section V.

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The study considers related work on ALO applications, 123 chaotic optimization, constraint handling techniques, and 124 petroleum scheduling. ALO has shown significant performance in both constrained 127 and unconstrained optimization problems. In an uncon-128 strained engineering problem like gear train design, ALO has 129 been utilized to optimize the parameter tuning [33]. ALO 130 has shown effectiveness in handling the Integrated Mainte-131 nance Scheduling problem [34]; optimal design in engineer-132 ing problems [    are available in the literature [24]. The popular methods are 182 the penalty function, separatist method, feasibility preserving 183 method, and hybrid approaches [24]. Penalty constrained 184 handling method converts the constraint to unconstraint by 185 incorporating a term called penalty to the objective function. 186 The solution consequently decreases the objective value [51]. 187 where γ (ū) and f (ū) represent the modified and original 189 objective functions respectively, h i and k j denotes the inequal-190 ity and equality constraints respectively, while q i and p j are 191 the penalty parameters [21], [51]. The penalty method is 192 broadly divided into two categories, interior and exterior 193 penalty methods. The exterior penalty approach requires the 194 knowledge of the feasible solution and it is not suitable for 195 many real-world problems. In the exterior penalty method, 196 on the contrary, the knowledge of the feasible solution is 197 not a prerequire [24]. The exterior penalty paradigm has 198 demonstrated effectiveness when integrated with the Genetic 199 Algorithm (GA) [24]. Various transportation means exist for shipping petroleum 202 products, including roads, vessels, railways, and pipelines. 203 Although the pipeline is the most economical, it is capital 204 intensive and less efficient [52]. The benefits of optimization 205 in refinery operations cannot be underestimated. Implicitly, 206 it determines the business is sustained amidst highly compet-207 itive and unstable environmental challenges. Enhancing the 208 planning and services of petroleum products is a paramount 209 management concern in the oil and gas industry [53]. In a 210 highly constrained and competitive environment, manage-211 ment and stakeholders need an efficient optimization model 212 to maximize profit [54]. Although some commercial tools 213   oil, kerosene, gasoline, wax, bitumen, and others) and eight 267 distribution centres. Also, the unit transportation cost of each 268 product from the source to the depot is given in the unit 269 cost row, while the total quantity of each product available is 270 presented in the availability column. The company operates 271 on certain policies. First, the distribution policy (policy row) 272 that states that a certain percentage of the product must be 273 sent to a depot to sustain customers' satisfaction and avoid 274 scarcity. Then the demand policy states that not more than the 275 requested amount of product should be shipped to a depot.

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TABLE 3 is an illustration of the quantity of each product 277 shipped to the eight depots. The zero quantity is highlighted 278 in red colour indicating that nothing was shipped to those 279 depots. By implication, the company policy is violated and it 280 could result in scarcity of those products at their correspond-281 ing location. Aside from policy violations, the total shipping 282 cost is relatively high. The present research attempts to satisfy 283 the constraints at reduced shipping costs.
. . , v i,n ) referred to the particle i 348 velocity, it is the distance to be covered by the particle from where m p ∈ (1, 0) and ψ is the parameter at (0,4) intervals. 370 Hence, Eq.(7) represents the chaotic PSO (CPSO). The antlion optimizer (ALO) was developed by Mirjalili in 378 2015. Its inspiration came from the hunting lifestyle of the 379 antlion [29]. The algorithm models the predator-prey rela-380 tionship between the antlion and the ants in the trap. Readers 381 are referred to [29] for the assumption that precedes the 382 ALO. The algorithm concept consists of six stages: the ants' 383 random motion stage, antlion trapping pits, trap construction, 384 descending of the ants towards the antlion, capturing prey 385 and pit reconstruction, and last, leader selection stage [29]. 386 The kernel of the algorithm is controlled using the following 387 equations. The random motion is represented by Eq. (8): where cumsum stands for the cumulative sum; u is the maxi-391 mum iteration, and k represents the random movement step; 392 r is a random number generator between zero and one. The 393 random motion is further normalized using Eq. (9). The nor-394 malization enables the search to be confined within the des-395 ignated search space.
where y i represents the i-th variable minimum random 398 motion; m i is the i-th variable maximum random motion; 399 while g u i is the maximum i-th variable at u-th iteration. The 400 descending and towards the antlion is represented by Eq. (10) 401 where F is a factor given by f = 10 p u u T where u is the current 404 iteration and u T is the maximum iteration, p is a constant and 405 it varies according to the maximum iteration [22]. Readers 406 could refer to (Mirjalili, 2015a) for more details about the 407 varying p-value. The last updating function is the Leadership 408 selection process based on the roulette wheel given by Eq. 11 409 where AP u i is the i-th position of the ant at iteration u-th; W u A is 411 the random motion within antlion based on the roulette wheel; 412 and W u L represents the random motion around the leader at the 413 u-th iteration. 414 VOLUME 10, 2022  The roulette wheel function is represented by eq.12: The convergence curve of the ALO algorithm is shown in 432 Fig. 3. Also, 99.5% of the constraints are satisfied; only one 433 is violated. The scheduling of the matrix shows that there is 434 no zero product, in contrast to the original (PPMC) supply 435 matrix in TABLE 3. It implies that the minimum quantity 436 supply policy is satisfied, consequently solving the petroleum 437 of possible scarcity.  The experimental results of the proposed methodologies 466 were obtained in the same environmental conditions. Specif-467 ically, in intel R Pentium R CPU N3510 @ 1.99 GHz proces-468 sor; 4.00 GB RAM; and windows 10 64 × 64 bit operating 469 system.

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ALO is considered cost-effective since it converges with less 472 computational power to reduce the original total distribution 473 cost by 24.8%. Typically, there are two limitations in the proposed study. 482 First, one of the constraints was relaxed to obtain the results. 483 Therefore, more robust constraint handling methods could 484 be a suggestion for further study. Secondly, although the 485 proposed stochastic ALO and CPSO algorithm could handle 486 more problem sizes than the available data, however, the data 487