Section: New Results

Decomposition-based optimization

  • A set-oriented decomposition algorithm for multi-objective optimization.

    Participants: B. Derbel and A. Liefooghe, external collaborators: H. Aguirre and K. Tanaka, Shinshu University (JAPAN); S. Verel, Univ. Littoral (FRANCE); Q. Zhang, City University (HONG KONG)

    The working principles of the well-established multi-objective evolutionary algorithm MOEA/D relies on the iterative and cooperative improvement of a number of single-objective sub-problems obtained by decomposition. Besides the definition of sub-problems, selection and replacement are, like in any evolutionary algorithm, the two core elements of MOEA/D. We argue that these two components are however loosely coupled with the maintained population. Thereby, in [24], we propose to re-design the working principles of MOEA/D by adopting a set-oriented perspective, where a many-to-one mapping between sub-problems and solutions is considered. Selection is then performed by defining a neighborhood relation among solutions in the population set, depending on the corresponding sub-problem mapping. Replacement is performed following an elitist mechanism allowing the population to have a variable, but bounded, cardinality during the search process. By conducting a comprehensive empirical analysis on a range of combinatorial multi- and many-objective nk-landscapes, we show that the proposed approach leads to significant improvements, especially when dealing with an increasing number of objectives. Our findings indicate that a set-oriented design can constitute a sound alternative for strengthening the practice of multi- and many-objective evolutionary optimization based on decomposition.

  • Parallel Pareto local search for multi-objective optimization.

    Participants: B. Derbel and A. Liefooghe, external collaborators: J. Shi and J. Sun, Xi'an Jiaotong University (CHINA); Q. Zhang, City University (HONG KONG)

    Pareto Local Search (PLS) is a simple, yet effective optimization approach dedicated to multi-objective combinatorial optimization. It can however suffer from a high computational cost, especially when the size of the Pareto optimal set is relatively large. Recently, incorporating decomposition in PLS had revealed a high potential, not only in providing high-quality approximation sets, but also in speeding-up the search process. In [30], using the bi-objective Unconstrained Binary Quadratic Programming (bUBQP) problem as an illustrative benchmark, we demonstrate some shortcomings in the resulting decomposition-guided Parallel Pareto Local Search (PPLS), and we propose to revisit the PPLS design accordingly. For instances with a priori unknown Pareto front shape, we show that a simple pre-processing technique to estimate the scale of the Pareto front can help PPLS to better balance the workload. Furthermore, we propose a simple technique to deal with the critically-important scalability issue raised by PPLS when deployed over a large number of computing nodes. Our investigations show that the revisited version of PPLS provides a consistent performance, suggesting that decomposition-guided PPLS can be further generalized in order to improve both parallel efficiency and approximation quality.

  • Archivers for the representation of the set of approximate solutions for MOPs.

    Participants: E-G. Talbi, external collaborators: O. Schutze, C. Hernandez (Computer Science Department, Cinvestav, MEXICO), Q. Sun, Y. Naranjani (School of Engineering University of California, USA), R. Xiong (Department of Mechanics, University Tianjin, CHINA)

    In this work we have addressed the problem of computing suitable representations of the set of approximate solutions of a given multi-objective optimization problem via stochastic search algorithms. For this, we have proposed different archiving strategies for the selection of the candidate solutions maintained by the generation process of the stochastic search process, and investigate them further on analytically and empirically. For all archivers we have provided upper bounds on the approximation quality as well as on the cardinality of the limit solution set. A comparative study on some test problems in order to visualize the effect of all novel archiving strategies has also been carried out [18].