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...ing the Pareto front of an arbitrary objective space Y is usually not practical because of its size, one needs to be less ambitious in general. Therefore, the ɛ-approximate Pareto set was proposed in=-= [23] as p-=-ractical solution concept as it not only represents all vectors Y ∗ but also consists of a smaller number of elements. The ɛ-approximatesFig. 10. The concept of ɛ-dominance and ɛ-Pareto fronts Pa...

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...current shape of the Pareto front approximation. However, thereby the actual global indicator changes during the run and potentially cycles can occur during the optimization process—a phenomenon, cf. =-=[12]-=-, that emerges with most algorithms. Cycling is not necessarily a problem in the biobjective case, but as the number of objectives increases, it is likely that this behavior causes difficulties. The a...

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...ccording to some probability distribution and mutated by flipping a randomly chosen bit. For Algorithm 1 we consider a uniform distribution for selecting the parent. An appropriate archiving strategy =-=[7]-=- is assumed to prevent the population from growing exponentially. For this study it suffices to ensure that a solution is only accepted if it has different objective values (line 7). 3.1 Running Time ...

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...regions of interest to be found simultaneously in a single simulation run. Moreover, the use of the ɛ-based selection strategy (which is also similar to the ɛ-dominance strategies suggested elsewhere =-=[15, 10]-=-) ensures a spread of solutions near the preferred Pareto-optimal regions. In the parlance of the classical reference point approach, the above procedure is equivalent to using a weight vector emphasi...

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...ove the convergence and diversity of a PSO approach used for multiobjective optimization. They also use a “turbulence” operator. In further work, the authors [9] studied the influence of ¡ -dominance =-=[10]-=- on MOPSO methods. ¡ -dominance is compared with existing clustering techniques for fixing the archive size and the solutions are compared in terms of computational time, convergence and diversity. In...

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...visit feasible solutions. Laumanns et al. proposed the concept of ɛ-dominance (ɛ-dominance uses the same concept as the α-dominance proposed earlier by Kokolo et al., i.e a relaxed from of dominance) =-=[82]-=-. They suggested this form of dominance to implement better archiving strategies that overcomes the difficulty of multiobjective evolutionary algorithms have in converging towards the optimal Pareto f...

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... goal is to find a broad distribution of Pareto-optimal solutions. The Bayesian multi-objective optimization algorithm (BMOA) (Laumanns & Ocenasek, 2002) uses a special selection operator, ǫ-archive (=-=Laumanns, Thiele, Deb, & Zitzler, 2002-=-), to both ensure that Pareto-optimal solutions are maintained over time and that diversity is maintained so that an approximation of the entire Pareto set is preserved. The selection operator works b...