A hyper-heuristic guided by a probabilistic graphical model for single-objective real-parameter optimization

Metaheuristics algorithms are designed to find approximate solutions for challenging optimization problems. The success of the algorithm over a given optimization task relies on the suitability of its search heuristics for the problem-domain. Thus, the design of custom metaheuristic algorithms leads to more accurate solutions. Hyper-heuristics (HH) are important tools commonly used to select low-level heuristics (LLHs) to solve a specific problem. HH are able to acquire knowledge from the problems where they are used. However, as other artificial intelligence tools it is necessary to identify how the knowledge affects the performance of the algorithm. One way to generate such knowledge is to capture interactions between variables using probabilistic graphical models such as Bayesian networks (BN) in conjunction with estimation of distribution algorithms (EDA). This article presents a method based on that used an EDA based on BN as a high-level selection mechanism for HH called Hyper-heuristic approach based on Bayesian learning and evolutionary operators (HHBNO). Here the knowledge is extracted form BN to evolve the sequences of LLHs in an online learning process by exploring the inter-dependencies among the LLHs. The proposes approach is tested over CEC’17 set of benchmark function of single-objective real-parameter optimization. Statical tests verifies that the HHBNO  presents competitive results in comparison with other metaheuristic algorithms with high performance in terms of convergence. The generated BN is further visually investigated to display the acquired knowledge during the evolutionary process, and it is constructed with the probabilities of each LLHs.