MOEA/D with adaptive operator selection for the environmental/economic dispatch problem

Adaptive Operator Selection (AOS) is a method used to dynamically determine which operator should be applied in an optimization algorithm based on its performance history. Upper Confidence Bound (UCB) algorithms have been successfully applied for this task due to its ability to tackle the Exploration versus Exploitation (EvE) dilemma presented on AOS. However, it is important to note that the use of UCB algorithms for AOS is still incipient on Multiobjective Evolutionary Algorithms (MOEAs) and many contributions can be made. The aim of this paper is to extend the study of UCB based AOS methods, applying it to a real world problem: the Environmental/Economic Load Dispatch (EELD). Three methods are proposed: MOEA/D-UCB1, MOEA/D-UCB-T and MOEA/D-UCB-V. In these proposals the UCB-based algorithms from the Multi-Armed Bandit (MAB) literature are combined with MOEA/D (MOEA based on decomposition), one of the most successful MOEAs. A pool of operators composed of four Differential Evolution operators is used. The proposed approaches are evaluated in three known instances of the multi-objective environmental/economic dispatch problem, formulated as a nonlinear constrained optimization problem with competing objectives. Experimental results demonstrate that MOEA/D-UCB1 and MOEA/D-UCB-T can be favorably compared with state-of-the-art algorithms reported in the literature for all considered instances.