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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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Designing a robust demand-differentiated platelet supply chain network under disruption and uncertainty

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2020年第8期11卷 3231-3258页

作者： Yaghoubi, Saeed Hosseini-Motlagh, Seyyed-Mahdi Cheraghi, Sara Larimi, Niloofar Gilani Iran Univ Sci & Technol Sch Ind Engn Tehran Iran

Managing platelets supply chain network has proved challenging. Besides stochastic demand, the high perishability of platelets and the diversity of their demands make the management more intricate. As a motivation to conduct this paper, we investigate a real-world case study facing a variety of platelet demands to satisfy. Being the first-ever study, we contribute a practical method for the efficient design and planning of a multiple platelet-derived products supply chain network. As the most perishable blood product, platelets need to be maintained fresh. Thus, we suggest a bi-objective model make a tradeoff relationship between the network costs and platelets' freshness. Further, we account for two realistic features that the products are categorized into three main types with respect to their application and lifetime, and hospitals are prioritized based on their specialty and the population of patients they cover. To cope with the uncertainty and objective multiplicity, we develop a mixed approach. The network robustness under uncertainty is controlled by a robust method and the Pareto solutions of the conflicting objectives are obtained via an interactive approach. Further, we take into account real-world scenarios that the network facilities may face disruptions and utilize a robust scenario-based approach to deal with the disruption scenarios. The results demonstrate that although simultaneous demand fluctuation and disruption increase both logistics costs and delivery time, the proposed model is capable of achieving robust solutions that a little increase in the logistic costs obtains a considerable reduction in the level of relative regret. Further, the network will benefit from a favorable saving in the logistic costs only by a little increase in the storage time.

关键词： Platelet supply chain multi-product multi-objective programming Robust optimization Disruption

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DESIGNING A CLOSED-LOOP SUPPLY CHAIN NETWORK AND PROVIDING A multi-objective MATHEMATICAL MODEL TO SELECT A THIRD-PARTY LOGISTICS COMPANY AND SUPPLIER SIMULTANEOUSLY

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INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING-THEORY APPLICATIONS AND PRACTICE 2020年第2期27卷 245-275页

作者： Ghoushchi, Saeid Jafarzadeh Hushyar, Iman Urmia Univ Technol Fac Ind Engn Orumiyeh Iran

In this study, a closed-loop supply chain network is designed. The solution for the applied model is determined in two phases. First, third-party logistics (3PLs) and external suppliers are selected by using grey theory. The outputs are the weight of 3PLs and suppliers. Second, a multi-objective mixed-integer linear programming model (MOMILP) is proposed. Through this model, 3PLs and suppliers are selected, and the optimal amount of returns to 3PLs and parts purchased from suppliers are determined. The proposed model considers the simultaneous selection of 3PLs and suppliers. The contribution of this study is a novel configuration of the multi-stage, multi-period, multi-product closed-loop supply chain network and 3PL and supplier selection by using grey theory, wherein a MOMILP is developed to implement the network and partner allocation. The supplier hub is utilized in the proposed network, which has rarely been accomplished in the previous literature. Finally, a numerical example is provided.

关键词： Supplier selection Reverse logistics Third-party logistics Grey theory multi-objective programming

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Optimizing over the properly efficient set of convex multi-objective optimization problems

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ANNALS OF OPERATIONS RESEARCH 2020年第2期295卷 575-604页

作者： Ghazli, Kahina Gillis, Nicolas Moulai, Mustapha Fac Math USTHB LaROMad Algiers Algeria Univ Bejaia Bejaia Algeria Univ Mons Fac Polytech Dept Math & Operat Res Mons Belgium

Optimizing over the efficient set of a multi-objective optimization problem is among the difficult problems in global optimization because of its nonconvexity, even in the linear case. In this paper, we consider only properly efficient solutions which are characterized through weighted sum scalarization. We propose a numerical method to tackle this problem when the objective functions and the feasible set of the multi-objective optimization problem are convex. This algorithm penalizes progressively iterates that are not properly efficient and uses a sequence of convex nonlinear subproblems that can be solved efficiently. The proposed algorithm is shown to perform well on a set of standard problems from the literature, as it allows to obtain optimal solutions in all cases.

关键词： multi-objective programming Convex optimization Properly efficient set Penalty approach

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A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 147卷 106646-106646页

作者： Li, Jun Wang, Lishuai Univ Elect Sci & Technol China Sch Management & Econ Chengdu 610054 Peoples R China

Since security return cannot be accurately estimated using past data, in this paper it is assumed to take values in a given ellipsoidal uncertainty set. This paper aims to discuss a robust multi-objective portfolio selection problem based on the minimax regret criterion under an ellipsoidal uncertainty sets, in which the two objective functions are the portfolio return to be maximized and the mean absolute deviation as a risk measure to be minimized. The robust counterpart formulation for the proposed model is firstly presented, then an algorithm based on the relaxation procedure is designed to solve the robust counterpart formulation with second-order cone constraints and infinite constraints. Finally, a practical example based on real market data is presented to illustrate the effectiveness of the proposed model and the algorithm. Compared with the traditional robust portfolio model based on minimax robustness, the robust minimax regret optimal solutions proposed in this paper have better performance on several evaluation criteria.

关键词： Robust optimization multi-objective programming Minimax regret Ellipsoidal uncertainty Portfolio optimization

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On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

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POSITIVITY 2022年第5期26卷 86-86页

作者： Alzalg, Baha Oulha, Amira Achouak Univ Jordan Dept Math Amman 11942 Jordan Ohio State Univ Dept Comp Sci & Engn Columbus OH 43210 USA Univ Bachir El Ibrahimi Dept Math Bordj Bou Arreridj 34000 Algeria

We present approximate solutions for the robust semi-infinite multi-objective convex symmetric cone programming problem. By using the robust optimization approach, we establish an approximate optimality theorem and approximate duality theorems for approximate solutions in convex symmetric cone optimization problem involving infinitely many constraints to be satisfied and multiple objectives to be optimized simultaneously under the robust characteristic cone constraint qualification. We also give an example to illustrate the obtained results in an important special case, namely the robust semi-infinite multi-objective convex second-order cone program.

关键词： Robust symmetric cone optimization Semi-infinite programming multi-objective programming Approximate optimality conditions Approximate duality theorems

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Efficient Fuzzy Goal programming Model for multi-objective Production Distribution Problem

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International Journal of Applied and Computational Mathematics 2018年第2期4卷 1-19页

作者： Gupta, Srikant Ali, Irfan Ahmed, Aquil Department of Statistics and Operations Research Aligarh Muslim University Aligarh UP India

This paper comprises of modelling and optimization of a production–distribution problem with the multi-product. The proposed model combined three well-known approaches, fuzzy programming, goal programming and interactive programming to develop an efficient fuzzy goal programming (EFGP) model for multi-objective production distribution problem (MOPDP). In this approach decision maker (DM) decide the goals and constructed membership functions for each objective, and they changed according to the iterative decision taken by the DM. The proposed EFGP model for MOPDP attempts to simultaneously minimize total transportation costs and total delivery time concerning inventory levels, available initial stock at each source, as well as market demand and available warehouse space at each destination, and the constraint on the total budget. The main aid of the proposed model is that its offerings an organized outline that enables fuzzy goal decision-making for solving the MOPDP under an uncertain environment. © 2018, Springer (India) Private Ltd., part of Springer Nature.

关键词： Fuzzy goal programming Interactive programming multi-objective programming Production–distribution problem

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Stochastic optimization for flow-shop scheduling with on-site renewable energy generation using a case in the United States

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 149卷 106812-106812页

作者： Wang, Shasha Mason, Scott J. Gangammanavar, Harsha Clemson Univ Dept Ind Engn Clemson SC 29634 USA Southern Methodist Univ Dept Engn Management Informat & Syst Dallas TX USA

On-site renewable energy provides great opportunities for manufacturing plants to reduce energy costs when faced with time-varying electricity prices. To efficiently utilize on-site renewable energy generation, production schedules and energy supply decisions need to be well investigated. In this paper, we present a two-stage, multi-objective stochastic program for flow shops with sequence-dependent setup. The first stage provides optimal schedules to minimize the total completion time. The second stage determines the energy supply decisions to minimize energy costs under a time-of-use electricity pricing scheme. The power demand of the production is met by on-site renewable generation, supply from the main grid, and energy storage system. An epsilon-constraint algorithm integrated with L-shaped method is proposed to analyze the problem. Sets of Pareto optimal solutions are provided for decision-makers. Our results show that the energy cost of setup operations is relatively high such that it cannot be ignored. Further, using solar or wind energy saves energy costs significantly. While, utilizing solar energy can reduce more.

关键词： Production scheduling Flow shop Renewable energy Stochastic programming multi-objective programming

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Reliability-Centered Maintenance Task Planning for Overhead Electric Power Distribution Networks

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JOURNAL OF CONTROL AUTOMATION AND ELECTRICAL SYSTEMS 2020年第5期31卷 1278-1287页

作者： Misari, Antonio R. Leite, Jonatas B. Piasson, Diego Mantovani, Jose Roberto Sanches Sao Paulo State Univ UNESP Elect Engn Dept Brasil Ave 56 BR-15385000 Ilha Solteira SP Brazil State Univ Mato Grosso UNEMAT BR-78390000 Barra Do Bugres MT Brazil

In this paper, it is presented an approach to match technically and economically the reliability of electricity distribution networks through an optimization methodology consisting of the mathematical model and metaheuristic solution technique to obtain an optimized plan for efficient management of maintenance tasks. The problem of maintenance tasks is formulated as a mixed dynamic nonlinear multi-objective optimization model, in which costs to perform maintenance tasks on equipment and/or components that make up the electric distribution network are minimized, while they have their reliability maximized. The constraints of this model are the individual and group electricity supply interruption duration and frequency indices, and availability of financial and human resources. The solution of this problem is obtained through a specialized non-dominated sorting genetic algorithm multi-objective metaheuristic, which provides a set of non-dominated solutions very close to the optimal Pareto frontier. Each solution at this frontier represents a maintenance plan able to assist the making decision of the operators in distribution companies for managing the maintenance crews.

关键词： NSGA-II Metaheuristic multi-objective programming Reliability Maintenance tasks Distribution systems

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Resilience Strategy Optimization for Large Aircraft Supply Chain Based on Probabilistic Language QFD

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INTERNATIONAL JOURNAL OF INFORMATION SYSTEMS AND SUPPLY CHAIN MANAGEMENT 2020年第4期13卷 23-46页

作者： Luo, Ya Zhu, Jian-jun Nanjing Univ Aeronaut & Astronaut Nanjing Peoples R China

This paper proposes an optimization model of supply chain resilience strategy for large passenger aircraft. A quality function deployment (QFD) framework is conducted to analyze the resilience of the large passenger aircraft supply chain, and the key parameters are characterized based on the probabilistic linguistic term. Then based on the output of the QFD framework an optimization model of the resilience strategy considering the stochastic disturbance faced by the supply chain is constructed. Taking the supply chain for large aircraft cockpit control display module as an example to illustrate the application steps and feasibility of the model, the results demonstrate that change of supply chain management responsibilities, implementing hierarchical management of suppliers, seeking coordinated implementation of inventory management mode, and improving the pre-risk identification system, play prominent roles in enhancing supply chain resilience, and the combination of different strategies can indeed enhance the supply chain resilience under the budget constraint.

关键词： multi-objective programming Probabilistic Linguistic Term Set (PLTS,) QFD Resilience Strategy Stochastic programming

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