Exploring the Pareto Frontier using Multi-Sexual Evolutionary Algorithms: an Application to a Flexible Manufacturing Problem

摘要

In multi-objective optimization (MOO) problems we need to optimize or at least satisfy many possibly conflicting objectives. For instance, in manufacturing planning we might want to minimize the cost and production time while maximizing the product's quality. We propose the use of evolutionary algorithms (EAs) to solve these problems. EAs are computer programs that generate solutions by simulating a Darwinian evolution. Solutions are represented as individuals in a population and are assigned scores according to a fitness function that determines their relative quality. Strong solutions are selected for reproduction, and pass their genetic material to the next generation. Weak solutions are removed from the population. The fitness function evaluates each solution and returns a related score. In MOO problems, this fitness function is vector-valued, i.e. it returns a value for each objective. Therefore, instead of a global optimum, we try to find the Pareto-optimal or non-dominated frontier. We use multi-sexual EAs with as many genders as optimization criteria. We have created new crossover and gender assignment functions, and experimented with various parameters to determine the best setting (yielding the highest number of non-dominated solutions.) These experiments are conducted using a variety of fitness functions, and the algorithms are later evaluated on a flexible manufacturing problem with total cost and time minimization objectives.