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118 C. Gil, R. Baños, M. G. Montoya, A. Márquez, and J. Ortegavying for incorporation into the archive. PESA implicitly maintains a hyper-grid division ofphenotype space which allows it to keep track of the crowding degree in different regionsof the archive. However, unlike both PAES and SPEA, selection in PESA is based on thiscrowding measure. Replacement (deciding what must leave the archive if it becomes overfull)is also based on a crowding measure.msPESA (Mixed Spreading between PESA and NSGA-II). A new algorithm, which is ahybrid version between PESA and NSGA-II is implemented in order to improve the conceptof spreading. In the design of msPESA, the goal was to eliminate the potential weaknesses ofother MOEAs and to create a powerful MOEA. The main characteristics of msPESA are:- It uses a variation of the fast non-dominated sorting algorithm of NSGA-II where onlyone front is calculated.- A new archiving strategy is implemented for the external population. Once a candidatehas entered the external archive, members of the archive which is dominated will notbe removed.If the archive temporarily exceeding the maximum size, one solution musttherefore be removed from the archive. The choice is made by first finding the maximalsqueeze factor [4] in the population, and removing an arbitrary chromosome which hasthis squeeze factor.43ZDT1msPESAPESANSGA−IISPEA2f22100 0.2 0.4 0.6 0.8 1f1Figure 2.Non-dominated solutions obtained using NSGA-II, SPEA2, PESA and msPESA on ZDT1.3. Experimental AnalysisIn this section we consider the issues necessary to compare the performance of these algorithmsover a set of benchmarks. The elaboration of a merit ranking between the variousmethods is not a trivial procedure. In general, an order of MOEA merit is impossible dueto the NFL Theorem [12], although it is possible to extract some results from the behavior ofeach algorithm. In this paper we have taken into account the proximity to the Pareto frontand the uniformity in the distribution of the solutions. In the search for an impartial, accuratecomparison that excludes the effects of chance, it is necessary to consider many aspects, andfor this reason we have made our own implementation of each algorithm, and all of themhave been integrated in the same platform. Since EAs are highly configurable procedures [1],