Section: New Results

Decomposition-based optimization

During the year 2019, we have investigated decomposition-based optimization in the decision space as well as in the objective space. In the decision space, we have considered discrete as well as continuous problems. For discrete problems, we have reinvestigated our interval-based decomposition approach proposed in [7] as a baseline to explore ultra-scale Branch-and-Bound algorithms using Chapel [13]. The contribution is presented in Section 7.3. For continuous problems, we have extended the geometric fractal decomposition-based approach [10] to multi-objective optimization [32] and importantly to parallel computing [17] to deal with scalability, one of the major scientific challenges as pointed out in Section 3.1. In the objective space, we have deeply studied in [23] the surrogate-assisted multi-objective optimization based on decomposition. The contributions are summarized in the following.

Parallel fractal decomposition for big continuous optimization problems

Participants : El-Ghazali Talbi [contact person] , Amir Nakib [Laboratoire Images, Signaux et Systèmes Intelligents (LISSI), Paris] , Léo Souquet [Laboratoire Images, Signaux et Systèmes Intelligents (LISSI), Paris] .

Fractal Decomposition Algorithm (FDA) is a metaheuristic that was recently proposed to solve high dimensional continuous optimization problems [10]. This approach is based on a geometric fractal decomposition which divides the search space while looking for the optimal solution. While FDA and its fractal decomposition has shown to be an effective optimization algorithm, its running time grows significantly as the problems dimension increases. To deal with this expensive computational time, a parallelized version of FDA, called Parallel Fractal Decomposition Algorithm (PFDA) is proposed in [17]. The focus is on parallelizing the exploration and exploitation phases of the original algorithm in a multi-threaded environment. The performances of PFDA are evaluated on the same Benchmark used to illustrate FDA efficiency, the SOCO 2011. It is composed of 19 functions with dimensions going from 50 to 5000. The results show that PFDA allows one to achieve similar performances as the original version with a significantly reduced computational time.

Deterministic multi-objective fractal decomposition

Participants : El-Ghazali Talbi [contact person] , Amir Nakib [Laboratoire Images, Signaux et Systèmes Intelligents (LISSI), Paris] , Léo Souquet [Laboratoire Images, Signaux et Systèmes Intelligents (LISSI), Paris] .

We have proposed in [32] a new deterministic Multi-objective Fractal Decomposition Algorithm (Mo-FDA). The original FDA [10] was designed for single-objective large-scale continuous optimization problems. It is based on a “divide-and-conquer” strategy and a geometric fractal decomposition of the search space using hyperspheres. In this work, a scalarization approach is used to deal with multi-objective problems. The performance of Mo-FDA is compared to state-of-the-art algorithms from the literature on classical benchmarks of multi-objective optimization.

Surrogate-assisted multi-objective optimization based on decomposition

Participants : Nicolas Berveglieri, Bilel Derbel, Arnaud Liefooghe, Hernan Aguirre [Shinshu University, Japan] , Kiyoshi Tanaka [Shinshu University, Japan] .

A number of surrogate-assisted evolutionary algorithms are being developed for tackling expensive multi-objective optimization problems. On the one hand, a relatively broad range of techniques from both machine learning and multi-objective optimization can be combined for this purpose. Different taxonomies exist in order to better delimit the design choices, advantages and drawbacks of existing approaches. On the other hand, assessing the relative performance of a given approach is a difficult task, since it depends on the characteristics of the problem at hand. In [23], we focus on surrogate-assisted approaches using objective space decomposition as a core component. We propose a refined and fine-grained classification, ranging from EGO-like approaches to filtering or pre-screening. More importantly, we provide a comprehensive comparative study of a representative selection of state-of-the-art methods, together with simple baseline algorithms. We rely on selected benchmark functions taken from the bbob-biobj benchmarking test suite, that provides a variable range of objective function difficulties. Our empirical analysis highlights the effect of the available budget on the relative performance of each approach, and the impact of the training set and of the machine learning model construction on both solution quality and runtime efficiency.