A υ-Constrained Matrix Adaptation Evolution Strategy With Broyden-Based Mutation for Constrained Optimization

Abhishek Kumar, Swagatam Das, Abhishek Kumar Misra, Devender Singh

Abstract: To solve the nonconvex constrained optimization problems (COPs) over continuous search spaces by using a population-based optimization algorithm, balancing between the feasible and infeasible solutions in the population plays an important role over different stages of the optimization process. To keep this balance, we propose a constraint handling technique, called the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\upsilon $ </tex-math></inline-formula> -level penalty function, which works by transforming a COP into an unconstrained one. Also, to improve the ability of the algorithm in handling several complex constraints, especially nonlinear inequality and equality constraints, we suggest a Broyden-based mutation that finds a feasible solution to replace an infeasible solution. By incorporating these techniques with the matrix adaptation evolution strategy (MA-ES), we develop a new constrained optimization algorithm. An extensive comparative analysis undertaken using a broad range of benchmark problems indicates that the proposed algorithm can outperform several state-of-the-art constrained evolutionary optimizers.