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Abstract. In general, Multi-objective Evolutionary Algorithms do not guarantee find solutions in the Pareto-optimal set. We propose a new approach for solving decomposable deceptive multi-objective problems that can find all solutions of the Pareto-optimal set. Basically, the proposed approach starts by decomposing the problem into subproblems and, then, combining the found solutions. The resultant approach is a Multi-objective Estimation of Distribution Algorithm for solving relatively complex multi-objective decomposable problems, using a probabilistic model based on a phylogenetic tree. The results show that, for the tested problem, the algorithm can efficiently find all the solutions of the Pareto-optimal set, with better scaling than the hierarchical Bayesian Optimization Algorithm and other algorithms of the state of art.

In the Multidimensional Knapsack Problem (MKP) there are items easily identifiable as highly (lowly) profitable and likely to be chosen (not chosen) to compose high-quality solutions. For all the other items, the Knapsack Core (KC), the decision is harder. By focusing the search on the KC effective algorithms have been developed. However, the true KC is not available and most algorithms can only rely on items' efficiencies. Chu & Beasley Genetic Algorithm (CBGA), for example, uses efficiencies in a repair-operator which bias the search towards the KC. This paper shows that, as the search progresses, efficiencies lose their descriptive power and, consequently, CBGA's effectiveness decreases. As a result, CBGA rapidly finds its best solutions and stagnates. In order to circumvent this stagnation, extra information about the KC should be used to implement specific operators. Since there is a correlation between marginal probabilities in a population and efficiencies, we show that KCs can be estimated from the population during the search. By solving the estimated KCs with CPLEX, improvements were possible in many instances, evidencing CBGA's weakness to solve KCs and indicating a promising way to improve GAs for the MKP through the use of KC estimates.