Simulation-based method for the optimization of multi-criteria stochastic models

This dissertation proposes a novel simulation-based multi-objective optimization (SimMOpt) method to find near-optimum solutions to complex systems characterized by: (a) stochastic behavior, (b) multiple objectives, (c) constraints and objective functions that are not limited to linear equalities/inequalities, (d) variability is modeled by replicated evaluations of objective functions or by performing discrete event simulation runs. Some techniques are implemented to improve the performance of the SimMOpt: (a) discretization of the Gaussian distribution to select decision variables and perturb solutions, (b) tracking matrix, (c) Pareto archived evolution strategy (PAES) coupled with hypothesis testing, (d) non-linear programming (NLP) methods, (e) return-to-base procedure, and (d) simultaneous perturbation of multiple variables from different sections in the solution vector.

This research work is grounded on three relevant applications to assess the performance of the proposed method and the extensions needed to handle difference problems. Three implementations that address different challenges were studied: (a) a highly-disrupted supply chain of short life-span agricultural products, (b) the setting of the parameters on a metal cutting machine, and (c) a biomass-to-refinery network design for enhanced biofuel production. The quality of the solutions obtained from the SimMopt is evaluated in terms of its capacity to solve instances that may become intractable using the benchmark methods and its hypervolume indicator. Two benchmark methods are used for comparison purposes: (a) a stochastic multi-objective minimum cost flow (SMMCF) (comparison criteria: number of scenarios that each method is capable of solving), (b) a genetic algorithm and a multi-objective simulated annealing (MOSA) – based algorithm (comparison criteria: percentage of random points in a hyper-cube that remain dominated by the front obtained from using each method), respectively.