Appl Intell https://doi.org/10.1007/s10489-017-1090-1 Electromagnetism-like mechanism with collective animal behavior for multimodal optimization Jorge G´ alvez 1 · Erik Cuevas 1 · Omar Avalos 1 · Diego Oliva 1 · Salvador Hinojosa 2 © Springer Science+Business Media, LLC 2017 Abstract Evolutionary Computation Algorithms (ECA) are conceived as alternative methods for solving complex optimization problems through the search for the global optimum. Therefore, from a practical point of view, the acquisition of multiple promissory solutions is especially useful in engineering, since the global solution may not always be realizable due to several realistic constraints. Although ECAs perform well on the detection of the global solution, they are not suitable for finding multi- ple optima in a single execution due to their exploration- exploitation operators. This paper proposes a new algo- rithm called Collective Electromagnetism-like Optimization (CEMO). Under CEMO, a collective animal behavior is implemented as a memory mechanism simulating natural animal dominance over the population to extend the orig- inal Electromagnetism-like Optimization algorithm (EMO) operators to efficiently register and maintain all possible Optima in an optimization problem. The performance of the proposed CEMO is compared against several multimodal schemes over a set of benchmark functions considering the evaluation of multimodal performance indexes typically found in the literature. Experimental results are statistically  Jorge G´ alvez jorge.galvez@cutonala.udg.mx 1 Departamento de Electr´ onica, Universidad de Guadalajara, CUCEI, Av. Revoluci´ on 1500, Guadalajara, Jalisco, Mexico 2 Departamento Ingenier´ ıa del Software e Inteligencia Artificial, Facultad Inform´ atica, Universidad Complutense de Madrid, 28040 Madrid, Spain validated to eliminate the random effect in the obtained solutions. The proposed method exhibits higher and more consistent performance against the rest of the tested multi- modal techniques. Keywords Evolutionary computation algorithms · Multimodal optimization · Collective animal behavior · Collective electromagnetism-like mechanism optimization 1 Introduction Optimization theory involves an optimal solution being obtained from a possible set of solutions that formulate a minimization/maximization problem [1]. The study field of optimization comprises many areas including science, engineering, economics, and others where a mathematical model needs to be built to represent its inherent dynamics [2]. Optimization techniques are broadly divided in deter- ministic (derivative-based) and stochastic [3]. Deterministic approaches theoretically guarantee the detection of global minima/maxima. However, deterministic methods present difficulties on multimodal optimization problems [4]. Under such restriction, traditional deterministic techniques are sus- ceptible to be trapped in local convexities obtaining subop- timal solutions. As an alternative to deterministic methods, stochastic procedures are search strategies which can oper- ate within multimodal surfaces improving the detection of global solutions without any assumption about the optimiza- tion problem and its analytical properties [5]. Recently, several stochastic methods known as Evolu- tionary Computation Algorithms (ECA) have been con- ceived by the abstraction of natural, biological or even social Published Version