Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Abstract

Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation in last two decades. This method is to transform a constrained optimisation problem into a multi-objective optimisation problem, then solve it by an evolutionary algorithm. In this paper, we propose a new multi-objective method for constrained optimisation, which is to convert a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective not. Then this multiobjective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called "wide gap". The "wide gap" problem means that an algorithm needs exponential time to cross between two fitness levels. We prove that using helper and equivalent objectives may 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. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms. The case study proves the efficiency of the helper and equivalent objective method for constrained optimisation.

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