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multi-objective infinite horizon optimal control problems: characterization of the Pareto fronts and Pareto solutions

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COMPUTATIONAL & APPLIED MATHEMATICS 2021年第8期40卷 1-24页

作者： Chorobura, Ana Paula Univ Fed Parana Postgrad Program Math CP 19081 BR-81531980 Curitiba Parana Brazil

In this paper, multi-objective infinite horizon optimal control problems with state constraints are investigated. First, a mono-objective auxiliary optimal control problem, free of state constraints, is introduced. The weak Pareto front of the multi-objective optimal problem is related to a set contained in the boundary of the zero level set of the value function of the auxiliary control problem. Moreover, a more detailed characterization of the Pareto front for the multi-objective problem is presented. In the infinite horizon context, the value function of the auxiliary optimal control problem satisfies a Hamilton-Jacobi-Bellman equation;however, it is not the unique solution. A semi-Lagrangian scheme, based on the Dynamic programming Principle, is considered to compute the value function of the auxiliary optimal control problem. Furthermore, optimal Pareto trajectory reconstruction is analyzed.

关键词： multi-objective programming Infinite horizon optimal control problem Trajectory reconstruction Semi-Lagrangian scheme

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Toward a robust optimal point selection: a multiple-criteria decision-making process applied to multi-objective optimization using response surface methodology

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ENGINEERING WITH COMPUTERS 2021年第4期37卷 2735-2761页

作者： Souza Rocha, Luiz Cello Rotela Junior, Paulo Aquila, Giancarlo de Paiva, Anderson Paulo Balestrassi, Pedro Paulo Fed Inst Educ Sci & Technol North Minas Gerais Management Dept Almenara MG Brazil Univ Fed Paraiba Prod Engn Dept Cidade Univ S-N BR-58051900 Joao Pessoa Paraiba Brazil Univ Fed Itajuba Inst Prod Engn & Management Itajuba MG Brazil

During the multi-objective optimization process, numerous efficient solutions may be generated to form the Pareto frontier. Due to the complexity of formulating and solving mathematical problems, choosing the best point to be implemented becomes a non-trivial task. Thus, this paper introduces a weighting strategy named robust optimal point selection, based on ratio diversification/error, to choose the most preferred Pareto optimal point in multi-objective optimization problems using response surface methodology. Furthermore, this paper proposes to explore a theoretical gap-the prediction variance behavior related to the weighting. The ratios Shannon's entropy/error and diversity/error and the unscaled prediction variance are experimentally modeled using mixture design and the optimal weights for the multi-objective optimization process are defined by the maximization of the proposed measures. The study could demonstrate that the weights used in the multi-objective optimization process influence the prediction variance. Furthermore, the use of diversification measures, such as entropy and diversity, associated with measures of error, such as mean absolute percent error, was determined to be useful in mapping regions of minimum variance within the Pareto optimal responses obtained in the optimization process.

关键词： multi-objective programming multi-criteria analysis Robust optimal point selection (ROPS) Diversification measures Error measures

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A TWO-STAGE SOLUTION APPROACH FOR PLASTIC INJECTION MACHINES SCHEDULING PROBLEM

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第3期17卷 1289-1314页

作者： Sarac, Tugba Sipahioglu, Aydin Ozer, Emine Akyol Eskisehir Osmangazi Univ Dept Ind Engn Meselik Campus TR-26040 Eskisehir Turkey Eskisehir Tech Univ Dept Ind Engn Iki Eylul Campus TR-26555 Eskisehir Turkey

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.

关键词： Plastic injection identical parallel machine scheduling multi-objective programming integer programming

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An Overview of the Cash Transportation Problem

An Overview of the Cash Transportation Problem

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International Conference on Decision Aid Sciences and Applications (DASA)

作者： Alaya, Houda Univ Tunis Tunis Business Sch Business Analyt & Decis Making Lab Tunis Tunisia IHE Paris Logist & Innovat Technol Res Ctr Paris France

ISBN: (纸本)9781665495011

One of the relatively new study topics in Vehicle Routing is the Cash Transportation Problem. This problem takes into consideration the security in planning vehicle routes. Few papers have focused on the cash transportation problem. Minimizing the travel cost and/or minimizing the transportation risk are the objective functions considered in these problems. This paper is the first overview of the cash transportation problem addressed in the literature. We classify these problems into two categories, mono-objective and multi-objective problems.

关键词： Vehicle Routing Problem multi-objective programming Cash transportation Cash-in-Transit

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Protection system planning in distribution networks with microgrids using a bi-level multi-objective and multi-criteria optimization technique

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ELECTRIC POWER SYSTEMS RESEARCH 2024年 228卷

作者： Reiz, Cleberton Leite, Jonatas B. Gouveia, Clara S. Javadi, Mohammad Sadegh Sao Paulo State Univ UNESP Dept Elect Engn Ilha Solteira SP Brazil Inst Syst & Comp Engn Technol & Sci INESC TEC Porto Portugal Sao Paulo State Univ UNESP BR-15385000 Ilha Solteira SP Brazil

Microgrids are able to improve several features of power systems, such as energy efficiencies, operating costs and environmental impacts. Nevertheless, microgrids' protection must work congruently with power distribution protection to safely take all advantages. This research contributes to enable their protection by proposing a bilevel method to simultaneously solve the allocation and coordination problems, where the proposed scheme also includes local protections of distributed energy resources. The uncertainties associated with generation and loads are categorized by the k-means method, as well. The non-dominated sorting genetic algorithm II is employed in the upper-level task to solve the protection and control devices allocation problem with two opposing objectives. In the lower-level task, a genetic algorithm ensures their coordination. Protection devices include reclosers and fuses from the network, and directional relays for the point of common coupling of microgrids, while control devices consist of remote-controlled switches. In contrast to related works, local devices installed at the point of coupling of distributed generation units are considered as well, such as voltage-restrained overcurrent relays and frequency relays. The optimal solution for the decision-maker is achieved by utilizing the compromise programming technique. Results show the importance of solving the allocation and coordination problems simultaneously, achieving up to $25,000 cost savings compared to cases that solve these problems separately. The integrated strategy allows the network operator to select the optimum solution for the protective system and avoid corrective actions afterward. The results also show the viability of the islanding operation depending on the decision maker's criteria.

关键词： Power distribution planning Microgrids Reliability Power system protection multi-objective programming Bi-level optimization

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A TWO-STAGE BI-LEVEL DECISION APPROACH FOR GREEN SUPPLY CHAIN DESIGN AND CLOUD VIRTUAL MACHINE PLACEMENT

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INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING-THEORY APPLICATIONS AND PRACTICE 2021年第5期28卷 529-540页

作者： Kao, Han-Ying Lan, Zih-Heng Huang, Chien-Hao Huang, Chia-Hui Natl Dong Hwa Univ Dept Comp Sci & Informat Engn Hualien Taiwan Natl Taipei Univ Business Dept Business Adm Taipei Taiwan

This study aims to establish an integrated model of green supply chain network design in cloud computing environments. In this study, two levels are defined: supply chain design and virtual machine allocation. In the proposed two-stage model, the supply chain network design decision (leader level) is solved in the first stage by considering three objectives . minimizing the total costs, minimizing the carbon emission, and maximizing the satisfaction level of service (minimizing the transportation lead time). In the second stage, considering the information demand from the leader level, the placement of virtual machines to the supply chain servers (follower level) is established by minimization of energy consumption and maximization of the effectiveness (minimization of the power wastage) of the physical machine. A case study and experiments are conducted to verify the performance of the proposed methods.

关键词： green supply chain design virtual machine placement bi-level decision modes two-stage decision approaches multi-objective programming

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Examining the potential of an irrigation work to improve sustainability in a rural area

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WATER SUPPLY 2021年第6期21卷 2959-2973页

作者： Ragkos, Athanasios Ambas, Vasileios Hellen Agr Org DIMITRA Agr Econ Res Inst Athens 11528 Greece Univ Western Macedonia Sch Agr Terma Kontopoulou 53100 Florina Greece

Irrigation works aim to increase the efficiency of water use and economic benefits for farmers. This study adopts a broader view and investigates their potential to contribute to the achievement of other sustainability objectives. In particular, the paper employs a multi-objective programming (MOP) model, which examines the possibilities to simultaneously achieve four conflicting objectives with the upgrade of an irrigation network in a rural area in Greece. The four objectives are maximization of economic result (economic sustainability) and of employment (social sustainability) as well as the minimization of agrochemical use and irrigation water consumption (environmental sustainability). The compromise is sought through different cropping patterns either by restructuring existing crops (Scenario 1) or by also introducing new crops (Scenario 2). The results show that solutions in Scenario 2 performs much better in all dimensions of sustainability, however large increases in economic performance and employment come with lower environmental gains. A Cost-Benefit Analysis shows that very few solutions yield positive Net Present Value and the investment could be halted if benefits relating to social and environmental sustainability are disregarded. Results are discussed in conjunction to the proposal of a new governance scheme, which could assume broader roles in supporting sustainable development.

关键词： cost-benefit analysis crop restructuring governance multi-objective programming public-private partnerships technical and economic data

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Solving multi-objective integer indefinite quadratic fractional programs

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ANNALS OF OPERATIONS RESEARCH 2021年第1-2期296卷 821-840页

作者： Mekhilef, Amal Moulai, Mustapha Drici, Wassila USTHB Fac Math Dept Operat Res BP 32 Algiers 16111 Algeria USTHB Fac Math LaROMaD Lab BP 32 Algiers 16111 Algeria

In this paper, we describe an exact algorithm for solving a multi-objective integer indefinite quadratic fractional maximization problem. The algorithm generates the whole set of efficient solutions of the above mentioned problem. We optimize at first one of the objective functions in the original feasible region;in an iterative way and through the introduction of auxiliary constraints (efficient cut or branching constraint), the same objective function is optimized over progressively restricted or separated parts of the original feasible region, each time we get a candidate solution for non dominated solution, the efficient set is updated, the process ends when there is no unexplored parts of the original domain. The proposed method is based on an efficient cut which allows to reduce the feasible set avoiding non efficient solutions, the simplex like algorithm to solve a mono objective quadratic fractional maximization problem, and the classical branch and bound technique for integer decision variables. We establish theoretical results which prove the effectiveness of this new exact method, for illustration, numerical experiments are reported.

关键词： multi-objective programming Integer programming Quadratic programming Fractional programming Efficient cut Branch and cut

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Optimal allocation of regional water resources based on multi-objective dynamic equilibrium strategy

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APPLIED MATHEMATICAL MODELLING 2021年 90卷 1183-1203页

作者： Feng, Jianghong Jinan Univ Sch Management 601 Huangpu Ave West Guangzhou Peoples R China

Raising water demand, insufficient freshwater resources and uneven precipitation are the main causes of water conflicts in the river basin. The main challenges in water resources allocation are the following: first, the uncertainty of water supply caused by climate change;second, the dynamic allocation of water resources is not considered;third, there is a lack of equitable water allocation, which may lead to intensified conflicts among the water user sectors. Based on the above challenges, a multi-objective dynamic programming optimal water resources allocation model under uncertainties is established in this paper, which could be a resolution for water disputes as it addresses simultaneously economic, social and environmental benefits. The proposed model considers maximizing the minimum satisfaction degree of each water sector, maximizing the utilization efficiency of water resources in the basin, and maximizing economic benefits. Satisfaction degree function is introduced to optimize water allocation equality in water use sectors (agricultural, domestic, and industrial sectors), and economic efficiency loss acceptance is integrated into the model constraints to control the economic loss corresponding to variations in water availability. In addition, a case study demonstrated the practicality and rationality of the proposed model, and the model results proposed herein show significantly help for a single river basin. Most importantly, the results show that model with dynamic constraint ensures a greater overall economic return for the entire basin, and a larger variation in water resources of sub-area leads to a larger maximum economic efficiency loss. Moreover, the proposed model herein is flexible and can be used in other developing countries/regions only by modifying the parameters according to the actual situation. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Water allocation multi-objective programming Satisfaction degree Economic benefit multi-stage decision

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Adaptation to seasonal drought in irrigation districts of south China: A copula-based fuzzy-flexible stochastic multi-objective approach for precise irrigation planning

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JOURNAL OF HYDROLOGY 2023年第PartA期625卷

作者： Yue, Qiong Cui, Ningbo Zhang, Fan Guo, Shanshan Jiang, Shouzheng Yu, Xiuyun Zhu, Bin Hohai Univ Coll Agr Sci & Engn Nanjing 211100 Peoples R China Sichuan Univ State Key Lab Hydraul & Mt River Engn Chengdu 610065 Peoples R China Sichuan Univ Coll Water Resource & Hydropower Chengdu 610065 Peoples R China Beijing Forestry Univ Sch Soil & Water Conservat Beijing 100083 Peoples R China Tsinghua Univ Dept Hydraul Engn State Key Lab Hydrosci & Hydraul Engn Beijing 100084 Peoples R China

The occurrence of seasonal drought has led to periodic water shortages in irrigation districts of south China, posing significant agricultural challenges on water and food security. Consequently, there is a pressing need for high-efficient water resources management from a sustainability perspective. To address this issue, a copulabased fuzzy-flexible stochastic multi-objective programming (CFSMP) model was proposed to facilitate irrigation planning under the combined influence of seasonal dry and wet conditions. The model was aimed to simultaneously achieve maximum economic benefit, water productivity and green water use efficiency, considering the economic, social, and environmental spheres of the irrigation district. The CFSMP model represented an innovative solution that was capable of (1) precisely describing the response of crop yield to water supply at ten-day time scale, which can be matched with practical irrigation demand;(2) characterizing joint distributions of seasonal dry and wet conditions of precipitation during different crop growth periods based on the copula function;(3) reconciling conflicts on objectives among economic, social, and environmental spheres of the irrigation district in complex and uncertain environments. The proposed model was applied to the Dongfeng Reservoir Irrigation District in south China. The downscaled ten-day Jensen water production functions of main grain and cash crops were fitted to recognize precise distributions of crop water demand and water sensitivity index. The Frank copula, with the smallest value of squared Euclidean distribution, was selected to describe the joint distribution of seasonal precipitation and gain insights into actual seasonal water availability and water scarcity. The results showed that the proposed model produced more water-saving and yieldpromoting irrigation planning policies than the current quota. The average water allocation of rice, wheat, maize, rape, and citrus decreased by 352.6 mm, 10

关键词： Seasonal drought South China Irrigation planning Copula multi-objective programming

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