Towards Analyzing Multimodality of Continuous Multiobjective Landscapes

Parallel Problem Solving From Nature – PPSN XV

Derbel

Vérel

et al. 2018

Pareto local optimal solutions (PLOS) are believed to highly influence the dynamics and the performance of multi-objective optimization algorithms, especially those based on local search and Pareto dominance. A number of studies so far have investigated their impact on the difficulty of searching the landscape underlying a problem instance. However, the community still lacks knowledge on the structure of PLOS and the way it impacts the effectiveness of multi-objective algorithms. Inspired by the work on local optima networks in single-objective optimization, we introduce a PLOS network (PLOS-net) model as a step toward the fundamental understanding of multi-objective landscapes and search algorithms. Using a comprehensive set of ρmnk-landscapes, PLOS-nets are constructed by full enumeration, and selected network features are further extracted and analyzed with respect to instance characteristics. A correlation and regression analysis is then conducted to capture the importance of the PLOS-net features on the runtime and effectiveness of two prototypical Pareto-based heuristics. In particular, we are able to provide empirical evidence for the relevance of the PLOS-net model to explain algorithm performance. For instance, the degree of connectedness in the PLOS-net is shown to play an even more important role than the number of PLOS in the landscape.

Section: Introductionmentioning

confidence: 99%

On Pareto Local Optimal Solutions Networks

Parallel Problem Solving From Nature – PPSN XV

Derbel

Vérel

et al. 2018

“…A second direction should try to extend our experimental analysis to additional problems, different neighborhoods and other order-preserving indicators, to corroborate that our conjectures indeed generalize as expected. Of particular interest is the extension of our work to LO-sets for continuous problems [4]. Furthermore, there are other factors that were not considered here, such as the size of the search space and the correlation between objectives.…”

Section: Discussionmentioning

confidence: 99%

Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference

Proceedings of the Genetic and Evolutionary Computation Conference

López-Ibáñez

Paquete

et al. 2018

Local search algorithms have shown good performance for several multi-objective combinatorial optimization problems. These approaches naturally stop at a local optimal set (LO-set) under given definitions of neighborhood and preference relation among subsets of solutions, such as set-based dominance relation, hypervolume or epsilon indicator. It is an open question how LO-sets under different set preference relations relate to each other. This paper reports an in-depth experimental analysis on multi-objective nk-landscapes. Our results reveal that, whatever the preference relation, the number of LO-sets typically increases with the problem non-linearity, and decreases with the number of objectives. We observe that strict LO-sets of bounded cardinality under set-dominance are LO-sets under both epsilon and hypervolume, and that LO-sets under hypervolume are LO-sets under set-dominance, whereas LO-sets under epsilon are not. Nonetheless, LO-sets under set-dominance are more similar to LO-sets under epsilon than under hypervolume. These findings have important implications for multi-objective local search. For instance, a dominance-based approach with bounded archive gets more easily trapped and might experience difficulty to identify an LO-set under epsilon or hypervolume. On the contrary, a hypervolume-based approach is expected to perform more steps before converging to better approximations.

“…Finally, one of the main landscape features in single-objective optimization is the number of local optima [8]. Although multimodality is still largely overlooked in the multi-objective optimization literature, where the number of objectives is seen as the main source of difficulty, few recent studies have revealed its impact on multi-objective search performance [13], [18], [20], [11].…”

Section: A Global Featuresmentioning

confidence: 99%

“…Of particular interest is the number and distribution of local optima in the landscape, i.e. multimodality and ruggedness [7], [8], [9], [10], [11]. These features are empirically related to instance hardness and algorithm efficiency, and provide significant insights into the interplay between the problem structure and the behavior of search algorithms and their working components.…”

Section: Introductionmentioning

confidence: 99%

Landscape-Aware Performance Prediction for Evolutionary Multiobjective Optimization

IEEE Trans. Evol. Computat.

Daolio²,

Vérel

et al. 2020

We expose and contrast the impact of landscape characteristics on the performance of search heuristics for black-box multi-objective combinatorial optimization problems. A sound and concise summary of features characterizing the structure of an arbitrary problem instance is identified and related to the expected performance of global and local dominancebased multi-objective optimization algorithms. We provide a critical review of existing features tailored to multi-objective combinatorial optimization problems, and we propose additional ones that do not require any global knowledge from the landscape, making them suitable for large-size problem instances. Their intercorrelation and their association with algorithm performance are also analyzed. This allows us to assess the individual and the joint effect of problem features on algorithm performance, and to highlight the main difficulties encountered by such search heuristics. By providing effective tools for multiobjective landscape analysis, we highlight that multiple features are required to capture problem difficulty, and we provide further insights into the importance of ruggedness and multimodality to characterize multi-objective combinatorial landscapes.