An evolution program for non-linear transportation problems

In this paper we describe main features of a Strongly Feasible Evolution Pr ogram (SFEP) designed to solve non-linear network flow problems. The progra m can handle non-linearities both in the constraints and in the objective f unction. The solutions procedure is based on a recombination operator in wh ich all parents in a small mating pool have equal chance of contributing th eir genetic material to offspring. When offspring is created with better fi tness value than that of the worst parent, the worst parent is discarded fr om the mating pool while the offspring is placed in it. The main contributi ons are in the massive parallel initialization procedure which creates only feasible solutions with simple heuristic rules that increase chances of cr eating 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 handli ng mixed integer problems with non-linearities in both constraints and the objective function. Tests were conducted on a number of previously publishe d transportation problems with 49 and 100 decision variables, which constit ute a subset of network flow problems. Convergence to equal or better solut ions was achieved with often less than one tenth of the previous computatio nal efforts.