A Memetic Algorithm for Global Optimization of Multimodal Nonseparable Problems

It is a big challenging issue of avoiding falling into local optimum especially when facing high-dimensional nonseparable problems where the interdependencies among vector elements are unknown. In order to improve the performance of optimization algorithm, a novel memetic algorithm (MA) called cooperative particle swarm optimizer-modified harmony search (CPSO-MHS) is proposed in this paper, where the CPSO is used for local search and the MHS for global search. The CPSO, as a local search method, uses 1-D swarm to search each dimension separately and thus converges fast. Besides, it can obtain global optimum elements according to our experimental results and analyses. MHS implements the global search by recombining different vector elements and extracting global optimum elements. The interaction between local search and global search creates a set of local search zones, where global optimum elements reside within the search space. The CPSO-MHS algorithm is tested and compared with seven other optimization algorithms on a set of 28 standard benchmarks. Meanwhile, some MAs are also compared according to the results derived directly from their corresponding references. The experimental results demonstrate a good performance of the proposed CPSO-MHS algorithm in solving multimodal nonseparable problems.

I. Introduction

In the past decade, many advanced evolutionary algorithms (EAs) were proposed. However, more efficient optimization algorithms are always needed for solving complex real-world engineering problems. In general, the unconstrained optimization problems that we are going to solve can be formulated as a -dimensional minimization problem as follows:

$$\begin{equation} \text {Min}~:~ f(X), \quad X = \left [{x_{1},x_{2},\ldots,x_{d},\ldots,x_{D}}\right ] \end{equation}$$ where is the vector to be optimized, is called the vector element, and is the number of parameters [1].