Benchmarking MO-CMA-ES and COMO-CMA-ES on the bi-objective bbob-biobj testbed

Proceedings of the Genetic and Evolutionary Computation Conference

et al. 2023

We present a surrogate-assisted multiobjective optimization algorithm. The aggregation of the objectives relies on the Uncrowded Hypervolume Improvement (UHVI) which is partly replaced by a linear-quadratic surrogate that is integrated into the CMA-ES algorithm. Surrogating the UHVI poses two challenges. First, the UHVI is a dynamic function, changing with the empirical Pareto set. Second, it is a composite function, defined differently for dominated and nondominated points. The presented algorithm is thought to be used with expensive functions of moderate dimension (up to about 50) with a quadratic surrogate which is updated based on its ranking ability. We report numerical experiments which include tests on the COCO benchmark. The algorithm shows in particular linear convergence on the double sphere function with a convergence rate that is 6-20 times faster than without surrogate assistance. CCS CONCEPTS• Mathematics of computing → Stochastic control and optimization; • Computing methodologies → Modeling methodologies; Model verification and validation.

Section: Resultsmentioning

confidence: 90%

“…with the reference point at (10,10). We initialize each 𝑥 0 uniformly at random in [−5, 5] 𝑑 and set the initial step size 𝜎 0 = 2/ √ 𝑑.…”

Section: Methodsmentioning

confidence: 99%

Multiobjective Optimization with a Quadratic Surrogate-assisted CMA-ES

Gharafi

Hansen

Proceedings of the Genetic and Evolutionary Computation Conference

et al. 2023

“…Otherwise, the performance is measured as the negative of the minimal distance of any found solution (in objective space and normalized as above) to the box [0, 1] 2 ; for details, seeBrockhoff et al (2016).23 All plots shown in this article have been prepared with COCO version 2.4 and the corresponding hypervolume reference values. Improved hypervolume reference values as well as the bbob-biobjext suite are available from version 3.0.24 Displayed is the performance of the three algorithms COMO-CMA-ES with a population size of 100 ("COMO-100",Touré et al, 2019;Dufossé and Touré, 2019), SMS-EMOA with differential evolution as search operator ("SMS-EMOA-DE",Beume et al, 2007;Auger et al, 2016b) and the MATLAB implementation of NSGA-II ("NSGA-II-Matlab",Deb et al, 2002;Auger et al, 2016a).…”

mentioning

confidence: 99%

Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites

Evolutionary Computation

Tušar

Auger

et al. 2022

Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, like wellunderstood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably under-represented in real-world problems such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Via the alternative construction of combining existing single-objective problems from the literature, we describe the bbob–biobj test suite with 55 biobjective functions in continuous domain, and its extended version with 92 biobjective functions (bbob–biobj–ext). Both test suites have been implemented in the COCO platform for black-box optimization benchmarking and various visualizations of the test functions are shown to reveal their properties. Besides providing details on the construction of these problems and presenting their (known) properties, this paper also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking.

DMS and MultiGLODS

Proceedings of the Genetic and Evolutionary Computation Conference Companion

Plaquevent-Jourdain

Auger

et al. 2021

Direct Multisearch (DMS) and MultiGLODS are two derivative-free solvers for approximating the entire set of Pareto-optimal solutions of a multiobjective (blackbox) problem. They both follow the search/poll step approach of direct search methods, employ Pareto dominance to avoid aggregating objectives, and have theoretical limit guarantees. Although the original publications already compare the two algorithms empirically with a variety of multiobjective solvers, an analysis on their scaling behavior with dimension was missing. Here, we run the publicly available implementations on the bbob-biobj test suite of the COCO platform and by investigating their performances in more detail, observe (i) a small defect in the default initialization of DMS, (ii) for both algorithms a decrease in relative performance to other algorithms of the original studies (even matching the performance of random search for MultiGLODS in higher dimension), and (iii) consequently, an under-performance to previously untested stochastic solvers from the evolutionary computation field, especially when the dimension is higher. CCS CONCEPTS• Computing methodologies → Continuous space search.