Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm

Many engineering problems require the optimization of expensive, black-box functions involving multiple conflicting criteria, such that commonly used methods like multiobjective genetic algorithms are inadequate. To tackle this problem several algorithms have been developed using surrogates. However, these often have disadvantages such as the requirement of a priori knowledge of the output functions or exponentially scaling computational cost with respect to the number of objectives. In this paper a new algorithm is proposed, TSEMO, which uses Gaussian processes as surrogates. The Gaussian processes are sampled using spectral sampling techniques to make use of Thompson sampling in conjunction with the hypervolume quality indicator and NSGA-II to choose a new evaluation point at each iteration. The reference point required for the hypervolume calculation is estimated within TSEMO. Further, a simple extension was proposed to carry out batch-sequential design. TSEMO was compared to ParEGO, an expected hypervolume implementation, and NSGA-II on 9 test problems with a budget of 150 function evaluations. Overall, TSEMO shows promising performance, while giving a simple algorithm without the requirement of a priori knowledge, reduced hypervolume calculations to approach linear scaling with respect to the number of objectives, the capacity to handle noise and lastly the ability for batch-sequential usage

Comparison of design concepts in multi-criteria decision-making using level diagrams

[EN] In this work, we address the evaluation of design concepts and the analysis of multiple Pareto fronts in multi-criteria decision-making using level diagrams. Such analysis is relevant when two (or more) design concepts with different design alternatives lie in the same objective space, but describe different Pareto fronts. Therefore, the problem can be stated as a Pareto front comparison between two (or more) design concepts that only differ in their relative complexity, implementation issues, or the theory applied to solve the problem at hand. Such analysis will help the decision maker obtain a better insight of a conceptual solution and be able to decide if the use of a complex concept is justified instead of a simple concept. The approach is validated in a set of multi-criteria decision making benchmark problems. © 2012 Elsevier Inc. All rights reserved.This work was partially supported by the FPI-2010/19 Grant and Project PAID-06-11 from the Universitat Politecnica de Valencia and by Projects ENE2011-25900, TIN2011-28082 (Spanish Ministry of Science and Innovation) and GV/2012/073, PROMETEO/2012/028 (Generalitat Valenciana).Reynoso Meza, G.; Blasco Ferragud, FX.; Sanchís Saez, J.; Herrero Durá, JM. (2013). Comparison of design concepts in multi-criteria decision-making using level diagrams. INFORMATION SCIENCES. 221(1):124-141. https://doi.org/10.1016/j.ins.2012.09.049S124141221

Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems

Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.Fil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Méndez, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

Evolutionary population dynamics and multi-objective optimisation problems

Griffith Sciences, School of Information and Communication TechnologyFull Tex

A Novel Multiobjective Formulation of the Robust Software Project Scheduling Problem

Chicano, F., Cervantes A., Luna F., & Recio G. (2012). A Novel Multiobjective Formulation of the Robust Software Project Scheduling Problem. (Di Chio, C., Agapitos A., Cagnoni S., Cotta C., de Vega F. Fernández, Di Caro G. A., et al., Ed.).Applications of Evolutionary Computation - EvoApplications 2012: EvoCOMNET, EvoCOMPLEX, EvoFIN, EvoGAMES, EvoHOT, EvoIASP, EvoNUM, EvoPAR, EvoRISK, EvoSTIM, and EvoSTOC, Málaga, Spain, April 11-13, 2012, Proceedings. 497–507.The Software Project Scheduling (SPS) problem refers to the distribution of tasks during a software project lifetime. Software development involves managing human resources and a total budget in an optimal way for a successful project which, in turn, demonstrates the importance of the SPS problem for software companies. This paper proposes a novel formulation for the SPS problem which takes into account actual issues such as the productivity of the employees at performing different tasks. The formulation also provides project managers with robust solutions arising from an analysis of the inaccuracies in task-cost estimations. An experimental study is presented which compares the resulting project plans and analyses the performance of four different well-know evolutionary algorithms over two sets of realistic instances representing the problem. Statistical parameters are also provided in order to help the project manager in the decision process.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04. Andalusian Government under contract P07-TIC-03044

How to Evaluate Solutions in Pareto-based Search-Based Software Engineering? A Critical Review and Methodological Guidance

With modern requirements, there is an increasing tendency of considering multiple objectives/criteria simultaneously in many Software Engineering (SE) scenarios. Such a multi-objective optimization scenario comes with an important issue -- how to evaluate the outcome of optimization algorithms, which typically is a set of incomparable solutions (i.e., being Pareto non-dominated to each other). This issue can be challenging for the SE community, particularly for practitioners of Search-Based SE (SBSE). On one hand, multi-objective optimization could still be relatively new to SE/SBSE researchers, who may not be able to identify the right evaluation methods for their problems. On the other hand, simply following the evaluation methods for general multi-objective optimization problems may not be appropriate for specific SE problems, especially when the problem nature or decision maker's preferences are explicitly/implicitly available. This has been well echoed in the literature by various inappropriate/inadequate selection and inaccurate/misleading use of evaluation methods. In this paper, we first carry out a systematic and critical review of quality evaluation for multi-objective optimization in SBSE. We survey 717 papers published between 2009 and 2019 from 36 venues in seven repositories, and select 95 prominent studies, through which we identify five important but overlooked issues in the area. We then conduct an in-depth analysis of quality evaluation indicators/methods and general situations in SBSE, which, together with the identified issues, enables us to codify a methodological guidance for selecting and using evaluation methods in different SBSE scenarios.Comment: This paper has been accepted by IEEE Transactions on Software Engineering, available as full OA: https://ieeexplore.ieee.org/document/925218