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A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2020年第1期75卷 263-290页

作者： Bento, Glaydston de Carvalho Barbosa Bitar, Sandro Dimy da Cruz Neto, Joao Xavier Soubeyran, Antoine de Oliveira Souza, Joao Carlos Univ Fed Goias IME Goiania Go Brazil Univ Fed Amazonas ICE Manaus Amazonas Brazil Univ Fed Piaui CCN DM Teresina PI Brazil Aix Marseille Univ Aix Marseille Sch Econ CNRS Aix En Provence France Aix Marseille Univ Aix Marseille Sch Econ EHESS Aix En Provence France

We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104-1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.

关键词： multi-objective programming Proximal point method DC function Variational rationality Behavioral sciences

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A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

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APPLIED MATHEMATICAL MODELLING 2014年第19-20期38卷 4897-4911页

作者： Li, Mo Guo, Ping China Agr Univ Ctr Agr Water Res China Beijing 100083 Peoples R China

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin's irrigation areas, Gansu Province, China. In this study, the irrigation areas' economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Irrigation water resources Optimal allocation multi-objective programming multiple uncertainties

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An evolutionary computation approach to solving repairable multi-state multi-objective redundancy allocation problems

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NEURAL COMPUTING & APPLICATIONS 2018年第1期30卷 127-139页

作者： Tavana, Madjid Khalili-Damghani, Kaveh Di Caprio, Debora Oveisi, Zeynab La Salle Univ Business Syst & Analyt Dept Distinguished Chair Business Syst & Analyt Philadelphia PA 19141 USA Univ Paderborn Business Informat Syst Dept Fac Business Adm & Econ D-33098 Paderborn Germany Islamic Azad Univ Dept Ind Engn South Tehran Branch Tehran Iran York Univ Dept Math & Stat Toronto ON Canada Polo Tecnol IISS G Galilei Bolzano Italy

The redundancy allocation problem (RAP) is an optimization problem for maximizing system reliability at a predetermined time. Among the several extensions of RAPs, those considering multi-state and repairable components are the closest ones to real-life availability engineering problems. However, despite their practical implications, this class of problems has not received much attention in the RAP literature. In this paper, we propose a multi-objective nonlinear mixed-integer mathematical programming to model repairable multi-state multi-objective RAPs (RMMRAPs) where a series of parallel systems experiencing repairs, partial failures, and component degrading through time is considered. The performance of a component depends on its state and may decrease/increase due to minor and major failures/repairs which are modeled by a Markov process. The proposed RMMRAP allows for configuring multiple components and redundancy levels in each sub-system while evaluating multiple objectives (i.e., availability and cost). A customized version of the non-dominated sorting genetic algorithm (NSGA-II), where constraints are handled using a combination of penalty functions and modification strategies, is introduced to solve the proposed RMMRAP. The performance of the proposed NSGA-II and that of an exact multi-objective mathematical solution procedure, known as the epsilon-constraint method, are compared on several benchmark RMMRAP instances. The results obtained show the relative dominance of the proposed customized NSGA-II over the epsilon-constraint method.

关键词： Redundancy allocation problem Availability computation Repairable component multi-state component Markov process multi-objective programming NSGA-II

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Optimal water allocation through a multi-objective compromise between environmental, social, and economic preferences

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ENVIRONMENTAL MODELLING & SOFTWARE 2015年 64卷 18-30页

作者： Roozbahani, Reza Schreider, Sergei Abbasi, Babak RMIT Univ Sch Math & Geospatial Sci Melbourne Vic 3001 Australia

Raising water demands and insufficient freshwater resources are the main reasons of water conflicts in transboundary watersheds. Sustainable water allocation can be a resolution for water disputes as it addresses simultaneously economic, social and environmental benefits. In this paper, a multi-objective model is introduced, which leads to sustainable water allocation of transboundary watersheds taking into account all these three aspects. Five water allocation objectives are proposed for this model in which three of them address the social factors and others represent the economic and environmental preferences. The Compromise programming technique is employed to solve the applied model to the Sefidrud Basin, Iran and several water allocation schemes are provided based on various weights combinations. The results of the model elucidate that the proposed model can allocate 83 percent of the Basin's water resources, to its stakeholders in a sustainable way while the environmental demand is satisfied. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Water allocation multi-objective programming Compromise programming Water allocation objectives

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A novel approach for distant wind farm interconnection: Iran South-West wind farms integration

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RENEWABLE ENERGY 2019年 140卷 737-750页

作者： Javadi, Mohammad Sadegh Razavi, Seyed-Ehsan Ahmadi, Abdollah Siano, Pierluigi Islamic Azad Univ Shiraz Branch Young Researchers & Elite Club Shiraz Iran Univ Birjand Dept Elect & Comp Engn Birjand Iran Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Univ Salerno Dept Ind Engn Fisciano Italy

A multi-objective wind farm integration framework is proposed in this paper which considers the composite generation and reliability assessment and annualized operating and investment cost evaluation. An emission-controlled policy is adopted such that the amount of SOx and NOx decreases in line with renewable resource planning. Since the incorporation of large-scale distant wind farms is a problem of the multi-objective mixed-integer type with nonlinearities and non-convexities, this paper utilizes a fast elicit multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA II) by probabilistic indices. It is noted that the impacts of the unavailability of the transmission system are modeled employing DC Optimal Power Flow (OPF) based on the incidence matrix together with the static security evaluation. Furthermore, in order to assess the performance of the suggested approach, the model is implemented on the Roy Billinton Test System (RBTS). Afterwards, distant wind farms integration into Iran's South-West Regional Grid (ISWRG) is studied. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Distant wind farm incorporation Combined generation and transmission reliability assessment Iran's South-West Regional grid multi-objective programming

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Optimal design of multi-reservoir systems for water supply

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ADVANCES IN WATER RESOURCES 2000年第6期23卷 613-624页

作者： Mousavi, H Ramamurthy, AS Seattle Publ Util Resource Planning Div Seattle WA 98104 USA Concordia Univ Dept Bldg Civil & Environm Engn Montreal PQ H3G 1M8 Canada

Several successful applications of optimal control theory based on the Pontryagin's minimum principle have been recorded in literature for optimizing the operating policy of multi-reservoir systems. However, the application of optimal control theory in sizing multi-reservoir systems resulted in sub-optimal solution. In this study, an optimization model based on a new composite algorithm is introduced. This model applies optimal control theory and penalty successive linear programming as two promising techniques to optimize large and complex water supply systems. The epsilon constraint approach was implemented in the model in order to consider the two non-commensurate objectives of minimizing cost and water deficit. The application of this model to a multi-reservoir system was compared to an existing dynamic programming model. The result of this study showed that the developed model is a very promising optimization method to design multi-reservoir systems regardless of their sizes. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： reservoirs water supply storage optimization design cost modeling multi-objective programming

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Mufti-objective optimal planning for designing relief delivery systems

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2007年第6期43卷 673-686页

作者： Tzeng, Gwo-Hshiung Cheng, Hsin-Jung Huang, Tsung Dow Kainan Univ Dept Business Adm Luchu 338 Taoyuan County Taiwan Kainan Univ Dept Informat Management Luchu 338 Taoyuan County Taiwan Natl Chiao Tung Univ Coll Management Inst Management Technol Hsinchu 300 Taiwan Natl Chiao Tung Univ Coll Management Inst Traff & Transportat Hsinchu 300 Taiwan

The fatal earthquake on September 21, 1999 caused significant damages to Taiwan, which made the national government focus on strengthening relief systems regarding natural disasters. Disaster prevention, protection, and reconstruction are the major areas of focus to reduce human suffering and damage from disasters. A key point is the ability to enhance the distribution of relief materials effectively. In this study, we construct a relief-distribution model using the mufti-objective programming method for designing relief delivery systems in a real case. The model features three objectives: minimizing the total cost, minimizing the total travel time, and maximizing the minimal satisfaction during the planning period. The first two objectives pursue the efficiency goal, whereas the third pursue fairness-making best effort to ensure relief commodity delivery to all demand points. Results of an empirical study are presented and suggestions are given for future research. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： earthquake multi-objective programming natural disaster relief distribution relief systems

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Coordinating efficiency and equity in disaster relief logistics via information updates

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2014年第8期45卷 1607-1621页

作者： Zhan, Sha-lei Liu, Nan Ye, Yong Zhejiang Univ Sch Management Dept Management Sci & Engn Hangzhou 310003 Zhejiang Peoples R China

This paper addresses a multi-supplier, multi-affected area, multi-relief, and multi-vehicle relief allocation problem in disaster relief logistics. A multi-objective optimisation model based on disaster scenario information updates is proposed in an attempt to coordinate efficiency and equity through timely and appropriate decisions regarding issues such as vehicle routing and relief allocation. An optimal stopping rule is also proposed to determine the optimum period of delay before responding to disaster, because decision making requires accurate disaster information. The main contribution of this paper is solving relief allocation problem in a novel way by correlating operational research with statistical decision making and Bayesian sequential analysis. Finally, a case is presented based on the post-disaster rescue in Eastern China after supertyphoon Saomai to test the applicability and show the potential advantages of the proposed model.

关键词： disaster relief logistics multi-objective programming information updates Bayesian sequential analysis optimal stopping problem

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An interactive heuristic method for multi-objective combinatorial optimization

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COMPUTERS & OPERATIONS RESEARCH 2000年第7-8期27卷 621-634页

作者： Teghem, J Tuyttens, D Ulungu, EL Fac Polytech Mons Lab Math & Operat Res B-7000 Mons Belgium

We have previously developed an adaptation of the simulated annealing for multi-objective combinatorial optimization (MOCO) problems to construct an approximation of the efficient set of such problem. In order to deal with large-scale problems, we transform this approach to propose an interactive procedure. The method is tested on the multi-objective knapsack problem and the multi-objective assignment problem. Scope and purpose Meta-heuristics methods are intensively used with success to solve optimization problems and especially combinatorial problems (Pirlot. EJOR 1996;92:493-511). In the case of a single objective problem, such methods compute an approximation to the unique optimal solution. Recently, some meta-heuristics have been adapted to treat multi-objective problems. These methods construct an approximation of the set of all efficient solutions. For large-scale multi-objective combinatorial problems, the number of efficient solutions may become very large. In order to help a decision maker to make a choice between these solutions, an interactive procedure is developed in this paper. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： multi-objective programming combinatorial optimization knapsack problem assignment problem simulated annealing

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multi-objective linear fractional inventory problem under intuitionistic fuzzy environment

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2019年第2期10卷 173-189页

作者： Ali, Irfan Gupta, Srikant Ahmed, Aquil Aligarh Muslim Univ Dept Stat & Operat Res Aligarh UP India

In this paper, we have assumed an inventory multi-objective optimization model under intuitionistic fuzziness. In modelling, we have considered the situations where triangular intuitionistic fuzzy numbers used to express some of the input information which associated with decision variables. Further, a ranking function approach by considering linear and the nonlinear degree of membership functions have been used to obtain the crisp form of the fuzzy parameters. Finally, the fuzzy goal programming approach has been used to solve the resultant model to obtain the optimal ordering quantity. Also, a comparative study of the formulated problem under intuitionistic fuzziness has been done with a deterministic model of inventory. The concept of the paper is explained through a numerical example.

关键词： Inventory problem multi-objective programming Linear fractional programming Intuitionistic fuzzy number Fuzzy goal programming

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