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)

Information to the eye of the beholder: data visualization for many-objective optimization

The visualization gap is one of the important challenges posed by many-objective optimization problems (MaOPs). In this paper, we present an integrated data visualization method for MaOPs, called CAP-vis plot, combining the Chord diagram, the Angular mapping and the Parallel coordinates in the same visualization. The method follows the circular design layout, showing different levels of information. This new approach allows the spatial location of points in high dimensional spaces, the visualization of harmony and conflict between objectives, as well as the comparison of the approximation sets provided by different algorithms. With this work, we try to fill the visualization gap and bring information to the eye of the decision-maker and the optimizer, with an intuitive overview of the obtained results. Some experiments were performed using the Benchmark Functions proposed for the IEEE-CEC 2018 Competition on Many-Objective Optimization. We used the tool to visualize the results obtained by NSGA-III, HypE, RVEA, MOEA/DD, PICEA-g, using the PlatEMO MATLAB platform, with the same parameter settings of the competition. The results on the Benchmark Problems show the importance of the qualitative analysis of the data. The experiments show how visualization can help interpretation of the results and identification of strengths and drawbacks of MOEA.The authors would like to thank the Brazilian agencies CAPES, CNPq and FAPEMIG for the financial support

Incorporation of region of interest in a decomposition-based multi-objective evolutionary algorithm

Preference-based Multi-Objective Evolutionary Algorithm (MOEA) restrict the search to a given region of the Pareto front preferred by the Decision Maker (DM), called the Region of Interest (ROI). In this paper, a new preference-guided MOEA is proposed. In this method, we define the ROI as a preference cone in the objective space. The preferential direction and the aperture of the cone are parameters that the DM has to provide to define the ROI. Given the preference cone, we employ a weight vector generation method that is based on a steady-state evolutionary algorithm. The main idea of our method is to evolve a population of weight vectors towards the characteristics that are desirable for a set of weight vectors in a decomposition-based MOEA framework. The main advantage is that the DM can define the number of weight vectors and thus can control the population size. Once the ROI is defined and the set of weight vectors are generated within the preference cone, we start a decomposition-based MOEA using the provided set of weights in its initialization. Therefore, this enforces the algorithm to converge to the ROI. The results show the benefit and adequacy of the preference cone MOEA/D for preference-guided many-objective optimization.This work was supported by the Brazilian funding agencies CAPES and CNPq

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Uma proposta de algoritmo baseado em cone de preferência para otimização com muitos objetivos e robusta

Submitted by Bruno Xavier ([email protected]) on 2019-11-22T16:19:14Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: cfd6801dba008cb6adbd9838b81582ab (MD5) PPGEngEletrica_IvanReinaldoMeneghini_TeseDOUTORADO.PDF: 17392954 bytes, checksum: 7341c60fe285f862be2eff1f3bf182df (MD5)Approved for entry into archive by Jane Campos ([email protected]) on 2019-11-22T16:48:24Z (GMT) No. of bitstreams: 2 license_rdf: 811 bytes, checksum: cfd6801dba008cb6adbd9838b81582ab (MD5) PPGEngEletrica_IvanReinaldoMeneghini_TeseDOUTORADO.PDF: 17392954 bytes, checksum: 7341c60fe285f862be2eff1f3bf182df (MD5)Made available in DSpace on 2019-11-26T17:17:17Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: cfd6801dba008cb6adbd9838b81582ab (MD5) PPGEngEletrica_IvanReinaldoMeneghini_TeseDOUTORADO.PDF: 17392954 bytes, checksum: 7341c60fe285f862be2eff1f3bf182df (MD5) Previous issue date: 2018-12-07CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorA solução de um problema de otimização multiobjetivo é um conjunto caracterizado pelo trade off ente M objetivos. No caso do problema de minimização F : RN ! RM, estas soluções de compromisso correspondem a um conjunto minimal segundo uma relação de ordem parcial no espaço RM. A busca por soluções de menor variação na presença de ruído nas variáveis x 2 RN caracteriza a Otimização Multiobjetivo Robusta. Este trabalho apresenta um algoritmo coevolutivo para Otimização Robusta. A proposta utiliza a estratégia de decomposição/agregação do espaço dos objetivos em um algoritmo coevolutivo competitivo. Em conjunto com esta nova técnica foi desenvolvido um novo método de geração de vetores de peso quase igualmente espaçados no espaço dos objetivos. Este novo método de geração de vetores de peso não apresenta limitação quanto ao número de vetores de peso criados nem quanto à norma de cada vetor, que podem estar localizados no primeiro ortante do espaço dos objetivos ou formar um cone de vetores com vértice na origem. O eixo deste cone corresponde a um vetor de preferências do tomador de decisão e sua abertura define a extensão da região de interesse escolhida. A qualidade dos vetores de peso produzidos por esta nova metodologia foi comparada com o método usual de geração de vetores de peso e os resultados se mostraram satisfatórios. Adicionalmente uma nova classe de problemas de otimização multiobjetivo foi desenvolvida, abrangendo otimização contínua e robusta, com e sem a presença de restrições de igualdade e desigualdade. Seguindo a estrutura utilizada na construção das funções de teste, uma nova métrica de avaliação de desempenho também é apresentada. A comparação dos resultados obtidos entre o método proposto e outras técnicas mostrou a superioridade dos métodos apresentados. Uma amostra dos resultados obtidos foi utilizada na ferramenta de visualização de dados desenvolvida, ilustrando as conclusões obtidasThe solution of a multi-objective optimization problem is a set characterized by the trade off of M objectives. In the case of the minimization problem F : R N → R M, these trade off solutions correspond to a minimal set according to a partial order relation in space R M. The search for solutions of smaller variation in the presence of noise in the variables x ∈ R N characterizes Robust Multiobjective Optimization. This work presents a co-evolutionary algorithm for Robust Optimization. The presented proposal uses the objective space decomposition/aggregation strategy in a competitive co-evolution algorithm. Along with this new technique, a new method of generating vectors of weight almost equally spaced in the objective space was developed. This new method of generating weight vectors is not limited in the number of weight vectors created neither to the norm of each vector, that can be located in the first orthant of the objective space to form a cone of vectors with vertex in the origin. The axis of this cone corresponds to a preference vector of the decision maker and its aperture defines the extension of the chosen region of interest. The quality of the weight vectors of weight produced by this new methodology was compared with the usual method of generation of weight vectors and the results were satisfactory. In addition, a new class of multi-objective optimization problems was developed, encompassing usual and robust optimization, with and without the presence of equality and inequality constraints. Following the structure used in the construction of the test functions, a new performance evaluation metric is also presented. The comparison of the results obtained between the proposed method and other techniques showed the superiority of the presented methods. A sample of the results obtained was used in the data visualization tool developed, showing the conclusions obtained

An adaptive multi-objective algorithm based on decomposition and large neighborhood search for a green machine scheduling problem.

Green machine scheduling consists in the allocation of jobs in order to maximize production, in view of the sustainable use of energy. This work addresses the unrelated parallel machine scheduling problem with setup times, with the minimization of the makespan and the total energy consumption. The latter takes into account the power consumption of each machine in different operation modes. We propose multi-objective extensions of the Adaptive Large Neighborhood Search (ALNS) metaheuristic with Learning Automata (LA) to improve the search process and to solve the large scale instances efficiently. ALNS combines ad-hoc destroy and repair (also named removal and insertion) operators and a local search procedure. The LA is used to adapt the selection of insertion and removal operators within the framework of ALNS. Two new algorithms are developed: the MO-ALNS and the MO-ALNS/D. The first algorithm is a direct extension of single objective ALNS by using multi-objective local search. As this method does not offer much control of the diversification of the Pareto front approximation, a second strategy employs the decomposition approach similar to MOEA/D algorithm. The results show that the MO-ALNS/D algorithm has better performance than MO-ALNS and MOEA/D in all indicators. These findings show that the decomposition strategy is beneficial not only for evolutionary algorithms, but it is indeed an efficient way to extend ALNS to multi-objective problems