Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Numerous multiobjective evolutionary algorithms (EAs) have been designed for constrained optimization over the past two decades. The idea behind these algorithms is to transform constrained optimization problems (COPs) into multiobjective optimization problems without any constraint, and then solve them. In this article, we propose a new multiobjective method for constrained optimization, which works by converting a COP into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that of the constrained problem but a helper objective does not. Then, this multiobjective optimization problem is decomposed into a group of subproblems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyze the computational time of the helper and equivalent objective method on a hard problem called ``wide gap.'' In a wide gap problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the wide gap. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. The experimental results show that its overall performance is ranked first when compared with other eight state-of-the-art EAs on IEEE CEC2017 benchmarks in constrained optimization.