On Ant Colony Optimization Algorithms for Multiobjective Problems

Many practically relevant problems have several objectives to be maximized or minimized, taking us into the area of Multiple Objective Optimization (MOO). In multi-objective optimization several conflicting objectives have to be simultaneously optimized. Therefore, there is usually no single solution which would give the best values for all the objective functions considered by the decision maker. Instead, in a typical MOO problem, there is a set of alternatives that are superior to the remainder when all the objectives are considered. This set of so-called non-dominated solutions is known as the Pareto optimum set, and provides many options for the decision-maker. Usually only one of these solutions is to be chosen. Due to the availability of and familiarity with single-objective optimizers, it is still common to combine all objectives into a single quantity to be optimized. Classical methods are usually based on reducing the multi-objective problem to a single objective one by combining (usually linearly) the objectives into one. It must be noted here that the (possibly conflicting) objectives are also non commensurable (cost, weight, speed, etc.), which makes it difficult to combine them into a single measure. As a result, those classical techniques have serious drawbacks (Coello et al., 2002); as they require a priori information about the problem (weights or thresholds), which are usually not available, and many runs are needed in order to obtain different solutions, since only one solution is obtained in each run. However, nowadays it is becoming clear that multi-objective problems can be successfully dealt with by employing a population based stochastic technique able to produce an approximation of the true set of non-dominated solutions in a single run. Due to the increasing complexity of the problems being tackled today, those methods are often based on nature-inspired metaheuristics such as evolutionary algorithms, particle swarm optimization, artificial immune systems, and ant colony optimization (ACO) (Gandibleux et al., 2004; Silberholz & Golden, 2009). Due to the good results obtained by ACO algorithms in a wide range of single-objective problems (Dorigo & Stützle, 2004) it is not surprising that several algorithms based on ACO have been proposed to solve multiple-objective problems. ACO is a constructive search technique to solve difficult combinatorial optimization problems, which is inspired by the behaviour of real ants. While walking, ants deposit pheromone on the ground marking a path that may be followed by other members of the colony. Shorter Jaqueline S. Angelo and Helio J.C. Barbosa Laboratório Nacional de Computação Cientı́fica LNCC/MCT Brasil On Ant Colony Optimization Algorithms for Multiobjective Problems 5