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In this chapter we are going to study metaheuristics based on the Automata Theory for the Multi-objective Optimization of Combinatorial Problems. As well known, Combinatorial Optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best possible solution(Yong-Fa & Ming-Yang, 2004). In this field it is possible to find a lot of problems denominated NP-Hard, that is mean that the problem does not have a solution in Polynomial Time. For instance, problems such as Multi-depot vehicle routing problem(Lim & Wang, 2005), delivery and pickup vehicle routing problem with time windows(Wang & Lang, 2008), multi-depot vehicle routing problem with weight-related costs(Fung et al., 2009), Railway Traveling Salesman Problem(Hu & Raidl, 2008), Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem(Oberlin et al., 2009) and Traveling Salesman with Multi-agent(Wang & Xu, 2009) are categorized as NP-Hard problems.

Evolutionary Algorithm based on the Automata Theory for the Multi-objective Optimization of Combinatorial Problems