Síťová simplex metoda vs. evoluční algoritmy

Abstract

This thesis addresses the solution of the multi-objective version of the Minimum Cost Flow problem, with an emphasis on comparing the classical deterministic approach and evolutionary metaheuristics. A bi-objective network simplex method is implemented, which systematically traverses the convex hull of the Pareto front and returns the complete set of feasible, non-dominated solutions, along with two variants of evolutionary algorithms, PTbNSGA-II and PTbMOEA/D, utilizing a probabilistic tree representation (PTbR) adapted for network problems. To visualize the optimization process, an interactive desktop tool was developed that enables step-by-step animation of the network simplex method and visualization of the Pareto front. Experimental evaluation on four instances reveals a profound performance duality between small instances—which reproduce the BiNSM optimal points and further densify the Pareto front in unsupported non-convex regions—and medium-sized instances, where the approximation capability of both metaheuristics drops dramatically.