Goal programming using multiple objective hybrid metaheuristic algorithm

Abstract

In this paper, a Goal Programming (GP) model is converted into a multi-objective optimization problem (MOO) of minimizing deviations from fixed goals. To solve the resulting MOO problem, a hybrid metaheuristic with two steps is proposed to find the Pareto set's solutions. First, a Record-to-Record Travel with an adaptive memory is used to find first non-dominated Pareto frontier solutions preemptively. Second, a Variable Neighbour Search technique with three transformation types is used to intensify every non dominated solution found in the first Pareto frontier to produce the final Pareto frontier solutions. The efficiency of the proposed approach is demonstrated by solving two nonlinear GP test problems and three engineering design problems. In all problems, multiple solutions to the GP problem are found in one single simulation run. The results prove that the proposed algorithm is robust, fast and simply structured, and manages to find high-quality solutions in short computational times by efficiently alternating search diversification and intensification using very few user-defined parameters.

Keywords:

• goal programming
• multi-objective optimization
• record-to-record travel algorithm
• adaptive memory
• variable neighbourhood search