A hybrid approach using TOPSIS, Differential Evolution, and Tabu Search to find multiple solutions of constrained non-linear integer optimization problems

This paper presents a novel method to find multiple solutions of multi-modal constrained non-linear integer optimization problems. First, the constrained optimization problem is cast into a bi-objective optimization problem, where the constraints are inserted as another objective function. Next, the novel method to solve multi-objective optimization problems is developed and applied to solve the reformulated problem. The novel method developed to solve multi-objective optimization problems is based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) whereas the multi-objective problem is cast in single-objectives problems. The Differential Evolution (DE) algorithm in its three versions (standard DE, DEbest and DEGL) are used as optimizer. Since the solutions found by the DE algorithms are continuous, a Tabu Searh (TS) is employed to find integer solutions during the optimization process. Experimental results show the effectiveness of the proposed method.