Abstract: Evolutionary computation (EC) is a category of algorithms which simulate the intelligent evolutionary behavior in nature for solving optimization problems. As EC algorithms do not rely on the mathematical characteristics of the problem model, they have been regarded as an important tool for complex optimization. Estimation of distribution algorithm (EDA) is a new class of EC algorithms, which works by constructing a probability model to estimate the distribution of the predominant individuals in the population, and sampling new individuals based on the probability model. With this probability-based search behavior, EDA is good at maintaining sufficient search diversity, and is applicable in both continuous and discrete search space. In order to promote the research of probability-based EC (PBEC) algorithms, this paper gives a survey on EC algorithms for multimodal optimization, and then further builds two frameworks for PBEC: PBEC framework for seeking multiple solutions in multimodal optimization, and PBEC framework for discrete optimization. The first framework presents a method to combine probability-based evolutionary operators with the niching strategy, so that higher search diversity can be maintained for seeking multiple solutions in multimodal optimization. In particular, the framework understands PBEC algorithms in a broad sense, that is, it allows both explicit PBEC algorithms (e.g. EDA) and implicit PBEC algorithms (e.g. ant colony optimization) to operate in the framework, resulting in two representative algorithms: multimodal EDA (MEDA) and adaptive multimodal ant colony optimization (AM-ACO). The second framework aims at extending the applicability of EC algorithms on both continuous and discrete space. Since some popular EC algorithms are originally defined on continuous real vector space and they cannot be directly used to solve discrete optimization problems, this framework introduces the idea of probability distribution based evolution and redefines their evolutionary operators on discrete set space. As a result, the applicability of these algorithms can be significantly improved.

Key words: probability distribution, evolutionary algorithm (EA), evolutionary computation (EC), multimodal optimization, computational intelligence