Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq); (ii) Coordination for the Improvement of Higher Education (CAPES) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese)

Evolutionary Dynamic Multi-Objective Optimisation : A survey

Peer reviewedPostprin

An Ensemble Surrogate-Based Framework for Expensive Multiobjective Evolutionary Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have become very popular for tackling computationally expensive multiobjective optimization problems (EMOPs), as the surrogate models in SAEAs can approximate EMOPs well, thereby reducing the time cost of the optimization process. However, with the increased number of decision variables in EMOPs, the prediction accuracy of surrogate models will deteriorate, which inevitably worsens the performance of SAEAs. To deal with this issue, this article suggests an ensemble surrogate-based framework for tackling EMOPs. In this framework, a global surrogate model is trained under the entire search space to explore the global area, while a number of surrogate submodels are trained under different search subspaces to exploit the subarea, so as to enhance the prediction accuracy and reliability. Moreover, a new infill sampling criterion is designed based on a set of reference vectors to select promising samples for training the models. To validate the generality and effectiveness of our framework, three state-of-the-art evolutionary algorithms [nondominated sorting genetic algorithm III (NSGA-III), multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) and reference vector-guided evolutionary algorithm (RVEA)] are embedded, which significantly improve their performance for solving most of the test EMOPs adopted in this article. When compared to some competitive SAEAs for solving EMOPs with up to 30 decision variables, the experimental results also validate the advantages of our approach in most cases

A Scalable Test Suite for Continuous Dynamic Multiobjective Optimization

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more importantly, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features are then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite are more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot

Comparative analysis of classical multi-objective evolutionary algorithms and seeding strategies for pairwise testing of Software Product Lines

Lopez-Herrejon, R. Erick, Ferrer J., Chicano F., Egyed A., & Alba E. (2014). Comparative analysis of classical multi-objective evolutionary algorithms and seeding strategies for pairwise testing of Software Product Lines. Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2014, Beijing, China, July 6-11, 2014. 387–396.Software Product Lines (SPLs) are families of related software products, each with its own set of feature combinations. Their commonly large number of products poses a unique set of challenges for software testing as it might not be technologically or economically feasible to test of all them individually. SPL pairwise testing aims at selecting a set of products to test such that all possible combinations of two features are covered by at least one selected product. Most approaches for SPL pairwise testing have focused on achieving full coverage of all pairwise feature combinations with the minimum number of products to test. Though useful in many contexts, this single-objective perspective does not reflect the prevailing scenario where software engineers do face trade-offs between the objectives of maximizing the coverage or minimizing the number of products to test. In contrast and to address this need, our work is the first to propose a classical multi-objective formalisation where both objectives are equally important. In this paper, we study the application to SPL pairwise testing of four classical multi-objective evolutionary algorithms. We developed three seeding strategies — techniques that leverage problem domain knowledge — and measured their performance impact on a large and diverse corpus of case studies using two well-known multi-objective quality measures. Our study identifies the performance differences among the algorithms and corroborates that the more domain knowledge leveraged the better the search results. Our findings enable software engineers to select not just one solution (as in the case of single-objective techniques) but instead to select from an array of test suite possibilities the one that best matches the economical and technological constraints of their testing context.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Austrian Science Fund (FWF) project P25289- N15 and Lise Meitner Fellowship M1421-N15. Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2011-28194 and fellowship BES-2012-055967. Project 8.06/5.47.4142 in collaboration with the VSB-Tech. Univ. of Ostrava and Universidad de Málaga, Andalucía Tech

Peeking beyond peaks: challenges and research potentials of continuous multimodal multi-objective optimization

Computer Systems, Imagery and Medi