Trust region based chaotic search for solving multi‐objective optimization problems

Abstract

A numerical optimization technique used to address nonlinear programming problems is the trust region (TR) method. TR uses a quadratic model, which may represent the function adequately, to create a neighbourhood around the current best solution as a trust region in each step, rather than searching for the original function's objective solution. This allows the method to determine the next local optimum. The TR technique has been utilized by numerous researchers to tackle multi‐objective optimization problems (MOOPs). But there is not any publication that discusses the issue of applying a chaotic search (CS) with the TR algorithm for solving multi‐objective (MO) problems. From this motivation, the main contribution of this study is to introduce trust‐region (TR) technique based on chaotic search (CS) for solving MOOPs. First, the reference point interactive approach is used to convert MOOP to a single objective optimization problem (SOOP). The search space is then randomly initialized with a set of initial points. Second, in order to supply locations on the Pareto boundary, the TR method solves the SOOP. Finally, all points on the Pareto frontier are obtained using CS. A range of MO benchmark problems have demonstrated the efficiency of the proposed algorithm (TR based CS) in generating Pareto optimum sets for MOOPs. Furthermore, a demonstration of the suggested algorithm's ability to resolve real‐world applications is provided through a practical implementation of the algorithm to improve an abrasive water‐jet machining process (AWJM).