A New Hybrid Metaheuristic for Equality Constrained Bi-objective Optimization Problems

COARSE-EMOA: An indicator-based evolutionary algorithm for solving equality constrained multi-objective optimization problems

“…The set of experiments performed consisted of a total of 20 independent runs of each algorithm per problem [19,54,55]. Each approximation was evaluated using two performance indicators to assess their quality and to quantify the number of feasible individuals found by the algorithms.…”

“…A recent approach from the work of Cuate et al [19] is the ✏ NSGA-II/PT, which considers the use of a hybrid EMOA for handling equality constraints. The authors propose the usage of a continuation strategy to refine the approximation obtained by an EMOA.…”

“…As a way to cope with constrained MOPs, many methods have been proposed ranging from the transformation of constraints into additional objectives to the incorporation of local search techniques and heuristics within EMOAs [10,11,12,13,14,15,16,17,18]. Nevertheless, many result in the inclusion of additional conditions for the problem to be solvable, by computing internal optimization problems or the calculation of gradients to obtain feasible solutions [14,19]. Moreover, in many situations, the existing methodologies and algorithms cannot achieve a full set of feasible solutions, some of them attaining no more than a 50% success rate [20].…”

A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs

“…The main challenge here is to avoid unnecessary effort, e.g., via computing non-optimal KKT points along local Pareto fronts that are already dominated by previously computed solutions. While this is relatively easy for k = 2 objectives (see [12]), this task becomes more complicated with increasing k. The following procedure works for general k.…”

“…We demonstrate the strength of the novel approach by showing results on selected benchmark problems and comparisons against some state-of-the-art MOEAs. A preliminary study of this work can be found in [12] which is restricted to the treatment of bi-objective problems, and where the discussion and comparison of the novel method is reduced.…”