A HYBRID MODIFIED SUBGRADIENT ALGORITHM THAT SELF-DETERMINES THE PROPER PARAMETER VALUES

Abstract

A successful solution algorithm for non-convex optimization problems is the Modified Subgradient Algorithm (MSGA), which solves dual problems based on the sharp augmented lagrangian function. However, its performance highly depends on its parameter values, and determining the appropriate parameter values is difficult as they can be completely different for each problem. In this study, a new hybrid solution approach that a tabu search algorithm to find the appropriate MSGA parameter values and the MSGA algorithm run together is proposed. Although it seems like a contradiction to use an algorithm that also has its parameters to determine the most appropriate parameter values of an algorithm, this contradiction is eliminated by fixing the parameter values of the tabu search algorithm. The proposed algorithm does not need appropriate values of any algorithm parameter. It can find appropriate parameter values for each problem itself starting with the same fixed initial values. To show the success of the developed algorithm, especially on 0-1 quadratic problems, it is compared with the classical MSGA algorithm by using the quadratic knapsack test instances taken in the literature. According to the obtained solutions, the superiority of the hybrid algorithm has been demonstrated.