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116 C. Gil, R. Baños, M. G. Montoya, A. Márquez, and J. Ortegak 2 k 1k 2 k 1dominatedindifferentworsesbetterindifferentnon−dominated(a)(b)Figure 1.Pareto-dominance relations.Pareto-optimal solutions in one single simulation run. Since the goal of approximating thePareto set is itself multiobjective, for instance, we would like to minimize the distance of thegenerated solutions to the Pareto set and to maximize the diversity of the achieved Paretoset approximation, then it is impossible to exactly describe what a good approximation is interms of a number of criteria such as closeness to the Pareto set, diversity, etc [10, 11]. In thefollowing, we present some general concepts of Multi-Objective Optimization.Definition 1. Multi-Objective Optimization (MOO) is the process of searching one ormore decision variables that simultaneously satisfy all constraints, and optimize an objectivefunction vector that maps the decision variables to two or more objectives.minimize/maximize(f k (s)), ∀k∈[1,K]subject to s∈FDefinition 2. Decision vector or solution (s) = (s 1 , s 2 , .., s n ) represents accurate numericalqualities for an optimization problem. The set of all decision vectors constitutes the decisionspace.Definition 3. Feasible set (F) is the set of decision vectors that simultaneously satisfies allthe constraints.Definition 4. Objective function vector (f) maps the decision vectors from the decisionspace into a K-dimensional objective space Z∈R K ,z=f(s), where: f(s)={f 1 (s), f 2 (s),..., f K (s)}, z∈Z, s∈F.Let P be a MOO problem, with K≥2 objectives. Instead of giving a scalar value to each solution,a partial order is defined according to Pareto-dominance relations, as we detail below.Definition 5. Order relation between decision vectors. Let s and s’ two decision vectors.The dominance relations in a minimization problem are:s dominates s’ (s≺s’) iff f(s)