An Evolution Program for Non-Linear Transportation Problems

Abstract

In this paper we describe main features of a Strongly Feasible Evolution Program (SFEP) designed to solve non-linear network flow problems. The program can handle non-linearities both in the constraints and in the objective function. The solutions procedure is based on a recombination operator in which all parents in a small mating pool have equal chance of contributing their genetic material to offspring. When offspring is created with better fitness value than that of the worst parent, the worst parent is discarded from the mating pool while the offspring is placed in it. The main contributions are in the massive parallel initialization procedure which creates only feasible solutions with simple heuristic rules that increase chances of creating solutions with good fitness values for the initial mating pool, and the gene therapy procedure which fixes “defective genes” ensuring that the offspring resulting from recombination is always feasible. Both procedures utilize the properties of network flows. The algorithm is capable of handling mixed integer problems with non-linearities in both constraints and the objective function. Tests were conducted on a number of previously published transportation problems with 49 and 100 decision variables, which constitute a subset of network flow problems. Convergence to equal or better solutions was achieved with often less than one tenth of the previous computational efforts.