Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) hold significant importance in resolving expensive optimization problems~(EOPs). Extensive efforts have been devoted to improving the efficacy of SAEAs through the development of proficient model-assisted selection methods. However, generating high-quality solutions is a prerequisite for selection. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thus impacting the quality of offspring solutions. This is a frequently encountered issue, yet it has not gained widespread attention. This paper presents a framework using unevaluated solutions to enhance the efficiency of SAEAs. The surrogate model is employed to identify high-quality solutions for direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models for the selection of the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to significantly enhance the efficiency of the algorithm.Comment: 18 pages, 9 figure

An Estimation of Distribution Algorithm With Cheap and Expensive Local Search Methods

In an estimation of distribution algorithm (EDA), global population distribution is modeled by a probabilistic model, from which new trial solutions are sampled, whereas individual location information is not directly and fully exploited. In this paper, we suggest to combine an EDA with cheap and expensive local search (LS) methods for making use of both global statistical information and individual location information. In our approach, part of a new solution is sampled from a modified univariate histogram probabilistic model and the rest is generated by refining a parent solution through a cheap LS method that does not need any function evaluation. When the population has converged, an expensive LS method is applied to improve a promising solution found so far. Controlled experiments have been carried out to investigate the effects of the algorithm components and the control parameters, the scalability on the number of variables, and the running time. The proposed algorithm has been compared with two state-of-The-art algorithms on two test suites of 27 test instances. Experimental results have shown that, for simple test instances, our algorithm can produce better or similar solutions but with faster convergence speed than the compared methods and for some complicated test instances it can find better solutions