A strongly feasible evolution program for non-linear optimization of network flows

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Ilich, Nesa
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This thesis describes the main features of a 'Strongly Feasible Evolution Program' ('SFEP') for solving network flow programs that can be non-linear both in the constraints and in the objective function. The approach is a hybrid of a network flow algorithm and an evolution program. Network flow theory is used to help conduct the search exclusively within the feasible region, while progress towards optimal points in the search space is achieved using evolution programming mechanisms such as recombination and mutation. The solution 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 an offspring. When an 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. Tests were conducted on a number of previously published transportation problems with 49 and 100 decision variables, and on two problems involving water resources networks with complex non-linear constraints with up to 1500 variables. Convergence to equal or better solutions was achieved with often less than one tenth of the previous computational efforts.