Editorial: Special issue on understanding complexity in multiobjective optimization

Abstract

This special issue of JMCDA was inspired by the work of three Dagstuhl seminars aimed at strengthening the links between the scientific communities of multiple criteria decision making (MCDM) and evolutionary multiobjective optimization. These three Dagstuhl seminars were devoted to the following topics:• Hybrid and robust approaches to multiobjective optimization Mutzel investigate complexity for multiobjective combinatorial optimization problems, taking into consideration output-sensitive complexity of an algorithm for a general enumeration problem, that is, the property that its running time is bounded by a polynomial in the input and the output size. The paper shows that output-sensitive complexity is able to separate efficiently solvable from presumably not efficiently solvable problems, proving also that multiobjective s-t-path problems do not admit an output-sensitive algorithm under weak complexity theoretic assumptions as P ≠ NP. Rodrigo Lankaites Pinheiro, Dario Landa-Silva, and Jason Atkin present a technique that supports understanding the relationships between objectives in a multiobjective optimization problem through a visualization and analysis of the local and global relationships between objectives. The advantages of the proposed technique are shown in experiments on three different combinatorial optimization problems (multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows).view of navigation, that is, the interactive procedure of traversing through a set of points (the navigation set) in the objective space guided by a decision maker, with the ultimate goal of identifying the single most preferred Pareto optimal solution. The authors describe a general framework to capture a wide range of navigation methods taking also into account real-world problems to which these methods have been applied and highlighting directions of future research. consider complex systems composed of strongly interrelated subsystems or subproblems with single or multiple objectives that are usually not sequentially ordered or obviously decomposable. In the literature, these systems are also referred to as "interwoven systems" or "systems of systems." Due to the correlation between the components, the overall system performance does not equal the simple sum of their performances, and inclusion of complex synergy may imply possible inaccuracies in the model and prohibitively expensive computations. The authors review recent developments in this field and present a preliminary mathematical model of an interwoven system introducing some approaches to its multiobjective optimization. start from the consideration that despite the fact that in general multiobjective combinatorial optimization problems are known to be hard problems because very often they are NP-complete and intractable, there are also variants or cases of multiobjective combinatorial optimization problems that are easy. The article focuses on particular cases of...

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