Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Efficient Hill Climber for Multi-Objective Pseudo-Boolean Optimization

Chicano, F., Whitley D., & Tinós R. (2016). Efficient Hill Climber for Multi-Objective Pseudo-Boolean Optimization. 16th European Conference on Evolutionary Computation for Combinatorial Optimization (LNCS 9595), pp. 88-103Local search algorithms and iterated local search algorithms are a basic technique. Local search can be a stand-alone search method, but it can also be hybridized with evolutionary algorithms. Recently, it has been shown that it is possible to identify improving moves in Hamming neighborhoods for k-bounded pseudo-Boolean optimization problems in constant time. This means that local search does not need to enumerate neighborhoods to find improving moves. It also means that evolutionary algorithms do not need to use random mutation as a operator, except perhaps as a way to escape local optima. In this paper, we show how improving moves can be identified in constant time for multiobjective problems that are expressed as k-bounded pseudo-Boolean functions. In particular, multiobjective forms of NK Landscapes and Mk Landscapes are considered.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Fulbright program, Ministerio de Educación (CAS12/00274), Ministerio de Economía y Competitividad (TIN2014-57341-R), Air Force Office of Scientific Research, Air Force Materiel Command, USAF (FA9550-11-1-0088), FAPESP (2015/06462-1) and CNPq