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An investigation into many-objective optimization on combinatorial problems: Analyzing the pickup and delivery problem

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SWARM AND evolutionary COMPUTATION 2018年 38卷 218-230页

作者： Garcia-Najera, Abel Lopez-Jaimes, Antonio Univ Autanoma Metropolitana Dept Matemat Aplicadas & Sistemas Unidad Cuajimalpa Av Vasco de Quiroga 4871Col Santa Fe Cuajimalpa Mexico City 05348 DF Mexico

Many-objective optimization focuses on solving optimization problems with four or more objectives. Effort has been made mainly on studying continuous problems, with interesting results and for which several proposals have appeared. An important result states that the problem does not necessarily becomes more difficult while more objectives are considered. Nevertheless, combinatorial problems have not received an appropriate attention, making this an open research area. This investigation takes this subject on by studying a many objective combinatorial problem, particularly, the pickup and delivery problem (PDP), which is an important combinatorial optimization problem in the transportation industry and consists of finding a collection of routes with minimum cost. Traditionally, cost has been associated with the number of routes and the total travel distance, however, in many applications, some other objectives emerge, for example, travel time, workload imbalance, and uncollected profit. If we consider all these objectives equally important, PDP can be tackled as a many-objective problem. This study is concerned with the study of: (i) the performance of four representative multi-objective evolutionary algorithms on PDP varying the number of objectives, (ii) the properties of the many-objective PDP regarding scalability, i.e. the conflict between each pair of objectives and the proportion of non-dominated solutions as the number of objectives is varied, and finally (iii) the change of PDP's difficulty when the number of objectives is increased. Results show that the regarded objectives are actually in conflict and that the problem is more difficult to solve while more objectives are considered.

关键词： Many-objective optimization Pickup and delivery problem multi-objective evolutionary algorithms Combinatorial optimization

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A hybrid project scheduling and material ordering problem: Modeling and solution algorithms

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APPLIED SOFT COMPUTING 2017年 58卷 700-713页

作者： Zoraghi, N. Shahsavar, A. Niaki, S. T. A. Islamic Azad Univ Fac Ind & Mech Engn Dept Ind Engn Qazvin Iran Sharif Univ Technol Dept Ind Engn Tehran Iran

A novel combination of a multimode project scheduling problem with material ordering, in which material procurements are exposed to the total quantity discount policy is investigated in this paper. The study aims at finding an optimal Pareto frontier for a triple objective model derived for the problem. While the first objective minimizes the makespan of the project, the second objective maximizes the robustness of the project schedule and finally the third objective minimizes the total costs pertaining to renewable and nonrenewable resources involved in a project. Four well-known multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm II (SPEAII), multi objective particle swarm optimization (MOPSO), and multi objective evolutionary algorithm based on decomposition (MOEAD) solve the developed triple-objective problem. The parameters of algorithms are tuned by the response surface methodology. The algorithms are carried out on a set of benchmarks and are compared based on five performance metrics evaluating their efficiencies in terms of closeness to the optimal frontier, diversity, and variance of results. Finally, a statistical assessment is conducted to analyze the results obtained by the algorithms. Results show that the NSGAII considerably outperforms others in 4 out of 5 metrics and the MOPSO performs better in terms of the remaining metric. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Material ordering multi-mode project scheduling multi-objective evolutionary algorithms Pareto frontier Total quantity discount

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multi-objective automatic calibration of SWAT using NSGA-II

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JOURNAL OF HYDROLOGY 2007年第3-4期341卷 165-176页

作者： Bekele, Elias G. Nicklow, John W. So Illinois Univ Dept Civil & Environm Engn Carbondale IL 62901 USA

This paper presents a diagnostic study on muttiobjective, automatic calibration of a physically based, semi-distributed watershed model known as Soil and Water Assessment Too[ (SWAT). Unlike lumped models, distributed models involve large number of calibration parameters, representing the spatial heterogeneity of inputs and various physical processes within a watershed. An automatic calibration routine is developed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) that has been proved to be an effective and efficient muttiobjective search technique in various applications. The automatic routine is capable of incorporating multiple objectives into the calibration process and also employs parameterization to help reduce the number of calibration parameters. In this study, SWAT is calibrated for daily streamftow and sediment concentration. Two calibration scenarios have been considered;the first scenario uses specific objective functions to fit different portions of the time series whereas in the second scenario, the calibration is performed using data from multiple gauging stations, simultaneously. In addition, two cases of parameter distribution have been considered in the second scenario during parameterization. The application results show that the approach is consistent and effective in estimating parameters of the model. The use of multiple objectives during the calibration process resulted in improved model performance and the second scenario, in particular, provided better results partly due to the respective location of the gauging stations within the watershed. Further distribution of parameters during parameterization also resulted in better sediment simulation. (c) 2007 Elsevier B.V. AR rights reserved.

关键词： distributed hydrologic models automatic calibration multi-objective evolutionary algorithms multiple calibration objectives

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Many-objective robust decision making for water allocation under climate change

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SCIENCE OF THE TOTAL ENVIRONMENT 2017年 607卷 294-303页

作者： Yan, Dan Ludwig, Fulco Huang, He Qing Werners, Saskia E. Wageningen Univ & Res Water Syst & Global Change POB 47 NL-6700 AA Wageningen Netherlands Chinese Acad Sci Inst Geog Sci & Nat Resources Res Key Lab Water Cycle & Related Land Surface Proc 11A Datun Rd Beijing 100101 Peoples R China

Water allocation is facing profound challenges due to climate change uncertainties. To identify adaptive water allocation strategies that are robust to climate change uncertainties, a model framework combining many-objective robust decision making and biophysical modeling is developed for large rivers. The framework was applied to the Pearl River basin (PRB), China where sufficient flow to the delta is required to reduce saltwater intrusion in the dry season. Before identifying and assessing robust water allocation plans for the future, the performance of ten state-of-the-art MOEAs (multi-objective evolutionary algorithms) is evaluated for the water allocation problem in the PRB. The Borg multi-objective evolutionary algorithm (Borg MOEA), which is a self-adaptive optimization algorithm, has the best performance during the historical periods. Therefore it is selected to generate new water allocation plans for the future (2079-2099). This study shows that robust decision making using carefully selected MOEAs can help limit saltwater intrusion in the Pearl River Delta. However, the framework could perform poorly due to larger than expected climate change impacts on water availability. Results also show that subjective design choices from the researchers and/or water managers could potentially affect the ability of the model framework, and cause the most robust water allocation plans to fail under future climate change. Developing robust allocation plans in a river basin suffering from increasing water shortage requires the researchers and water managers to well characterize future climate change of the study regions and vulnerabilities of their tools. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multi-objective evolutionary algorithms Climate uncertainties Robust decision making Pearl River basin

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Insights on surface wave dispersion and HVSR: Joint analysis via Pareto optimality

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JOURNAL OF APPLIED GEOPHYSICS 2010年第2期72卷 129-140页

作者： Giancarlo, Dal Moro Rhein Westfal TH Aachen GUtech Aachen Germany

Surface Wave (SW) dispersion and Horizontal-to-Vertical Spectral Ratio (HVSR) are known as tools able to provide possibly complementary information useful to depict the vertical shear-wave velocity profile. Their joint analysis might then be able to overcome the limits which inevitably affect such methodologies when they are singularly considered. When a problem involves the optimization (i.e. the inversion) of two or more objectives, the standard practice is represented by a normalized summation able to account for the typically different nature and magnitude of the considered phenomena (thus objective functions). This way, a single cost function is obtained and the optimization problem is performed through standard solvers. This approach is often problematic not only because of the mathematically and physically inelegant summation of quantities with different magnitudes and units of measurements. The critical point is indeed represented by the inaccurate performances necessarily obtained while dealing with problems characterized by several local minima and the impossibility of a rigorous assessment of the goodness and meaning of the final result. In the present paper joint analysis of both synthetic and field SW dispersion curves and HVSR datasets is performed via the Pareto front analysis. Results show the relevance of Pareto's criterion not only as ranking system to proceed in heuristic optimization (evolutionary algorithms) but also as a tool able to provide some insights about the characteristics of the analyzed signals and the overall congruency of data interpretation and inversion. Possible asymmetry of the final Pareto front models is discussed in the light of relative non-uniqueness of the two considered objective functions. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Joint inversion Surface wave dispersion HVSR Shear-wave velocity multi-objective evolutionary algorithms Rayleigh waves

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Robust active shock control bump design optimisation using hybrid parallel MOGA

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COMPUTERS & FLUIDS 2013年第1期80卷 214-224页

作者： Lee, D. S. Bugeda, G. Periaux, J. Onate, E. CIMNE Barcelona 08034 Spain Univ Politecn Cataluna ES-08034 Barcelona Spain Deloitte Analyt Deloitte Consulting LLC Seoul South Korea

The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a multi-objective evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFDs) software. For MOEA, Robust multi-objective Optimisation Platform (RMOP) developed at CIMNE is used. For the active shock control bump design, two different optimisation methods are considered;the first method is a Pareto-Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. Numerical results show not only how the concept of Shock Control Bump (SCB) coupled to CFD can improve aerodynamic performance of classic transonic aerofoil at the variability of flight conditions but also how high performance (parallel/distributed) computation with applying Hybrid-Game increases the efficiency of optimisation in terms of computational cost and results accuracy. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Robust/uncertainty design multi-objective evolutionary algorithms Game strategies Parallel computation Computational fluid dynamics Shock control bump

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multi-objectivization, fitness landscape transformation and search performance: A case of study on the hp model for protein structure prediction

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期243卷 405-422页

作者： Garza-Fabre, Mario Toscano-Pulido, Gregorio Rodriguez-Tello, Eduardo CINVESTAV Tamaulipas Informat Technol Lab Cd Victoria 87130 Tamaulipas Mexico

multi-objectivization represents a current and promising research direction which has led to the development of more competitive search mechanisms. This concept involves the restatement of a single-objective problem in an alternative multi-objective form, which can facilitate the process of finding a solution to the original problem. Recently, this transformation was applied with success to the HP model, a simplified yet challenging representation of the protein structure prediction problem. The use of alternative multi-objective formulations, based on the decomposition of the original objective function of the problem, has significantly increased the performance of search algorithms. The present study goes further on this topic. With the primary aim of understanding and quantifying the potential effects of multi-objectivization, a detailed analysis is first conducted to evaluate the extent to which this problem transformation impacts on an important characteristic of the fitness landscape, neutrality. To the authors' knowledge, the effects of multi-objectivization have not been previously investigated by explicitly sampling and evaluating the neutrality of the fitness landscape. Although focused on the HP model, most of the findings of such an analysis can be extrapolated to other problem domains, contributing thus to the general understanding of multi-objectivization. Finally, this study presents a comparative analysis where the advantages of multi-objectivization are evaluated in terms of the performance of a basic evolutionary algorithm. Both the two- and three-dimensional variants of the HP model (based on the square and cubic lattices, respectively) are considered. (C) 2014 Elsevier B.V. All rights reserved.

关键词： multi-objectivization Fitness landscape analysis Protein structure prediction Hydrophobic-polar model multi-objective evolutionary algorithms

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Environmental and economic power dispatch of thermal generators using modified NSGA-II algorithm

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2015年第8期25卷 1552-1569页

作者： Muthuswamy, Rajkumar Krishnan, Mahadevan Subramanian, Kannan Subramanian, Baskar Natl Coll Engn Dept EEE Tirunelveli 627151 Tamil Nadu India PSNA Coll Engn & Technol Dept EEE Dindigul 624622 Tamil Nadu India Kalasalingam Univ Dept EEE Krishnankoil 626126 Tamil Nadu India Thiagarajar Coll Engn Dept EEE Madurai 625015 Tamil Nadu India

This paper presents the solution to the problem in fabricating Environmental and Economic Power Dispatch (EEPD) of thermal generators with valve-point loading effect and multiple prohibited operating zones (POZ). The valve-point effect introduces ripples in the input-output characteristics of generating units, and the existence of POZ breaks the operating region of a generating unit into isolated sub-regions, thus forms a nonconvex decision space. The EEPD problem becomes a nonsmooth optimization problem because of these valve-point effect and POZ. Accuracy of the solution for a practical system is improved by considering the nonlinearities of valve-point loading effect and multiple POZ in the EEPD problem. The multi-objective evolutionary algorithms, namely non-dominated sorting genetic algorithm-II (NSGA-II) and modified NSGA-II (MNSGA-II) have been applied for solving the multi-objective nonlinear optimization EEPD problem. To improve the uniform distribution of non-dominated solutions, dynamic crowding distance is considered in the NSGA-II and developed MNSGA-II. These multi-objective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus and IEEE 118-bus test systems. Real-coded genetic algorithm is used to generate reference Pareto-front, which is used to compare with the Pareto front obtained using NSGA-II and MNSGA-II. Numerical results reveal that MNSGA-II is effectively capable for appreciable performance than NSGA-II to solve the different power system nonsmooth EEPD problem. Moreover, three different performance metrics such as convergence, diversity and Inverted Generational Distance are calculated for the evaluation of closeness of obtained Pareto fronts to the reference Pareto-front. In addition, an approach based on Technique for ordering Preferences by Similarity to Ideal Solution is applied to extract best compromise solution from the obtained non-domination solutions. Copyright (c) 2014 John Wiley & Sons, L

关键词： environmental and economic power dispatch valve-point effect prohibited operating zones multi-objective evolutionary algorithms modified non-dominated sorting genetic algorithm-II TOPSIS non-dominated solutions

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One decade of multi-objective calibration approaches in hydrological modelling: a review

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HYDROLOGICAL SCIENCES JOURNAL-JOURNAL DES SCIENCES HYDROLOGIQUES 2010年第1期55卷 58-78页

作者： Efstratiadis, Andreas Koutsoyiannis, Demetris Natl Tech Univ Athens Sch Civil Engn Dept Water Resources & Environm Engn GR-15780 Zografos Greece

One decade after the first publications on multi-objective calibration of hydrological models, we summarize the experience gained so far by underlining the key perspectives offered by such approaches to improve parameter identification. After reviewing the fundamentals of vector optimization theory and the algorithmic issues, we link the multi-criteria calibration approach with the concepts of uncertainty and equifinality. Specifically, the multi-criteria framework enables recognition and handling of errors and uncertainties, and detection of prominent behavioural solutions with acceptable trade-offs. Particularly in models of complex parameterization, a multi-objective approach becomes essential for improving the identifiability of parameters and augmenting the information contained in calibration by means of both multi-response measurements and empirical metrics ("soft" data), which account for the hydrological expertise. Based on the literature review, we also provide alternative techniques for dealing with conflicting and non-commeasurable criteria, and hybrid strategies to utilize the information gained towards identifying promising compromise solutions that ensure consistent and reliable calibrations.

关键词： multi-objective evolutionary algorithms multiple responses uncertainty equifinality hybrid calibration soft data

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A NOVEL multi-objective ESTIMATION OF DISTRIBUTION ALGORITHM BASED ON SENSITIVITY OF objective FUNCTION

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2013年第6期9卷 2543-2566页

作者： Seo, Hyunshik Lee, Chaewoo Ajou Univ Dept Elect & Comp Engn San 5 Suwon 443749 South Korea

Most multi-objective optimization problems (MOPs) have a set of optimal trade-off solutions known as the Pareto-optimal solutions since the objectives in MOPs are usually in conflict with one another. Recently proposed estimation of distribution algorithms (EDAs) build a probability distribution model based on the probabilistic information about decision variables of solutions, and then produce new solutions from the model. In the algorithms, the modeling technique enables the initial large search space to be reduced to small promising solution space during the search. However, the existing EDAs might be inefficient at generating the promising solutions since they depend on the information extracted from the decision variables of current solutions expected to approach the optimal solutions. For effective modeling of the promising solutions, we firstly introduce new information about the relationship between decision variables and objective functions;this information is called sensitivity of objective function. Secondly, we propose a multi-objective estimation of distribution algorithm based on the sensitivity of objective function (MOEDA-S). In the MOEDA-S, the sensitivity-based distribution modeling adapts to the current search strategy such that the convergence-focused search at the beginning part of the search is changed to a diversity-focused search at the latter part of the search. MOEDA-S is compared with two other leading multi-objective evolutionary algorithms on a set of test instances. The simulation results show that MOEDA-S outperforms the two compared algorithms in terms of both convergence and diversity performances of the solutions.

关键词： multi-objective optimization problems multi-objective evolutionary algorithms Estimation of distribution algorithms Variables sensitivity-based modeling

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