Multi-Objective Optimization of Mixed-Integer Programming Problems through a Hybrid Genetic Algorithm with Repair Operation

Abstract

We have concerned, in this paper, with developing a practical method for multi-objective mixed-integer programming problems. To cope with the problem in the hierarchical framework, we have already proposed the hybrid genetic algorithm incorporated with a modeling method of a value function using neural networks. In its master problem, genetic algorithm will solve the unconstrained discrete optimization using the neural network model of the value function, and mathematical program will solve the slave problem given as the constrained continuous optimization. Due to such good matches between the solution methods and the problem properties, the hybrid strategy can derive the best-compromise solution very effectively while the so far methods were limited to derive the Pareto optimal solution set. Furthermore, we have proposed a repair operation of genetic algorithm which models the mechanism of DNA in nature. It enables us to reduce the search space in genetic algorithm and the derived best-compromise solution to be a Pareto optimal solution. Hence, we can improve both the efficiency and the reliability in solution much more compared with the foregoing method.To examine effectiveness of the proposed method in an actual application, we have concerned with a site location problems of hazardous wastes disposal. As known from the term NIMBY (Not In My Back Yard), it is an eligible case study associated both with environmental and economic concerns. After describing the problem generally as a multi-objective mixed-integer linear program, through numerical experiments, we have confirmed the proposed method can derive the best-compromise solution effectively. In addition, we have shown the repair operation of genetic algorithm can work better compared with a penalty function approach against the inactive e-constraints and the foregoing method paying no concern on it.