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Logarithmic quasi-distance proximal point scalarization method for multi-objective programming

APPLIED MATHEMATICS AND COMPUTATION 2016年 273卷 856-867页

作者： Rocha, Rogerio Azevedo Oliveira, Paulo Roberto Gregorio, Ronaldo Malheiros Souza, Michael Tocantins Fed Univ Undergrad Computat Sci Course BR-77001090 Palmas Brazil Univ Fed Rio de Janeiro Comp & Syst Engn Dept BR-2194590 Rio De Janeiro Brazil Rio de Janeiro Fed Rural Univ Technol & Languages Dept BR-26221010 Rio De Janeiro Brazil Univ Fed Ceara Dept Stat & Appl Math BR-60455760 Fortaleza Ceara Brazil

Recently, Gregorio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al, as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance. By restricting it to a certain class of quasi-distances that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence { (x(k), z(k)) subset of R-n x R-m generated by the method satisfies: {z(k)} is convergent: and {x(k)} is bounded and its accumulation points are weak Pareto solutions of the unconstrained multi-objective optimization problem (C) 2015 Elsevier Inc. All rights reserved.

关键词： Proximal point algorithm Scalar representation multi-objective programming Quasi-distance

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A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期173卷 387-404页

作者： Islam, Sahidul Roy, Tapan Kumar Bengal Engn Coll DU Dept Math Howrah 711103 W Bengal India

In this paper, we introduce a fuzzy mathematical programming with generalized fuzzy number as objective coefficients. We also examine a transportation problem with additional restriction. There is an additional entropy objective function in the transportation problem besides transportation cost objective function. Using new fuzzy mathematical programming, this multi-objective entropy transportation problem with generalized trapezoidal fuzzy number costs has been reduced to a primal geometric programming problem. Pareto optimal solution of the transportation model is found. Numerical examples have been provided to illustrate the problem. (c) 2005 Elsevier B.V. All rights reserved.

关键词： multi-objective programming transportation entropy generalized fuzzy number geometric programming

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Using a multi-objective programming model to validate feasibility of an underground freight transportation system for the Yangshan port in Shanghai

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2018年 81卷 463-471页

作者： Chen, Yicun Guo, Dongjun Chen, Zhilong Fan, Yiqun Li, Xiao Army Engn Univ PLA Res Ctr Underground Space Nanjing 210007 Jiangsu Peoples R China Shanghai Municipal Engn Design Inst Grp Co Shanghai 200092 Peoples R China

Preventing environmental deterioration and alleviating traffic congestion are becoming urgent problems in urban and transportation planning. Alleviating the pressure from increasing freight transportation traffic via low-emission and innovative transportation methods can reduce problems such as transportation network capacity limits and environmental pollution and contribute to the development of resource-efficient and sustainable cities in the future. Underground freight transportation systems (UFTSs) can improve service quality and transportation efficiency in urban logistics and alleviate traffic congestion and associated problems such as energy consumption and air pollution. Previous studies on urban UFTSs have focused mostly on technical feasibility and policy requirements. Studies providing a quantitative analysis of the effects of introducing a UFTS on an existing transportation network are scarce. In this study, the main goal is to create a quantitative method to analyze the effects of introducing a UFTS on the performance of a transportation network. Thus, a multi-objective programming model of an integrated aboveground-underground transportation network that considers transportation cost, time, and emissions is created. The Yangshan port in Shanghai, China is used as an example to assess whether a UFTS can significantly reduce the cost, time, distance and emissions of the aboveground freight container transportation. The weights on three objective functions are varied to analyze their effects on the solution. These results provide a reference for optimizing freight distribution plans when a UFTS is constructed and for implementing integrated aboveground-underground transportation systems in the future.

关键词： Underground freight transportation system Integrated network multi-objective programming

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UNCERTAIN multi-objective programming MODEL OF TOURIST ROUTE CONSIDERING TOURIST PREFERENCE

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第8期20卷 2640-2651页

作者： Huang, Zheng Ning, Yufu Liu, Fengming Shandong Normal Univ Business Sch Jinan Peoples R China Shandong Youth Univ Polit Sci Sch Informat Engn Jinan Peoples R China Univ Shandong Smart Healthcare Big Data Engn & Ubiquitous Comp C Jinan Peoples R China

. Tourists going out for a trip encounter various uncertainties, such as weather conditions, road conditions, the tourists' consumption budget, travel time, and other uncertainties. Tourists focus on the goals of minimizing travel time and consumption costs while maximizing personal satisfaction with the route;therefore, the multi-objective programming model for an uncertain tourism route problem is established based on uncertainty theory. The objectives of the model are to minimize the travel time and consumption cost and to maximize the tourists' satisfaction with the route. According to inverse uncertainty distribution, the model can be transformed into a traditional programming model and solved by the ant colony algorithm (ACO). Finally, in order to solve the uncertain tourism route programming problem, a numerical example is given to show the application of the model.

关键词： Tourist route programming multi-objective programming uncertainty theory preference

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Aubin property for solution set in multi-objective programming

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第2期85卷 441-460页

作者： Rahimi, Morteza Soleimani-damaneh, Majid Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran Kharazmi Univ Fac Math Sci & Comp Tehran Iran

In this paper, the behavior of the solutions of a multi-objective optimization problem, whose the objective functions are perturbed by adding a small linear term, is analyzed. In this regard, a new notion of Lipschitzian stability, by means of the Aubin property of the solution set, is defined. Lipschitz stable locally efficient solutions, as generalization of tilt/full stable solutions, are introduced and characterized by modern variational analysis tools. Applying the weighted sum method, the relationships between these solutions and full-stable local optimal solutions of the scalarized problem are investigated. The key tools in deriving our results come from the first- and second-order variational analysis.

关键词： Variational analysis Perturbation in optimization multi-objective programming Aubin stability Tilt-stability Full-stability

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Evaluation of environmentally benign production program in the textile-dyeing industry (II): a multi-objective programming approach

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CIVIL ENGINEERING AND ENVIRONMENTAL SYSTEMS 2008年第1期25卷 1-28页

作者： Wu, Chia-Chin Chang, Ni-Bin Univ Cent Florida Dept Civil & Environm Engn Orlando FL 32816 USA Univ So Calif Dept Biomed Engn Los Angeles CA 90089 USA

The ways for improving a cost-effective industrial production program described in an earlier paper primarily focused on the quality assurance/quality control (QA/QC) schemes within the manufacturing stage. However, industry with high demand of resources input must evolve the essential production strategies to meet the goals in an environmentally benign production program. This paper describes the method and procedure for optimizing a textile-dyeing manufacturing process with respect to the potential impact of pollution charges, resources conservation fees, production cost, inventory cost, and the limitations of production capacity simultaneously. The optimal production strategy concerning numerous screening processes of those production alternatives in terms of market demand, production technology, and resources allocation is treated as an integral part in the multi-objective decision analysis. Facing the growing impact of rising environmental costs and the awareness of implications of industrial ecology, the case-study designed for a textile-dyeing factory in Central Taiwan demonstrates the application potential of a multi-objective evaluation method. It also emphasizes that the employed cost-effectiveness assessment framework can not only consider the conventional costs but also include the hidden costs, such as emission/effluent charges and water resources conservation fees to address the impacts of economic instruments. The research findings clearly indicate that apart from the concern of conventional cost accounting, enterprises facing the challenge of new environmental regulations and policy, which are designed to internalize the external cost in the society, and changing production requirements should employ such an optimal production assessment to enhance their competitiveness.

关键词： industrial ecology environmental management multi-objective programming pollution charge environmental cost resources valuation production planning

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Fuzzy multi-objective programming algorithm for vehicle routing problems with backhauls

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EXPERT SYSTEMS WITH APPLICATIONS 2015年第13期42卷 5632-5644页

作者： Yalcin, Gulcin Dinc Erginel, Nihal Anadolu Univ Fac Engn Dept Ind Engn TR-26555 Eskisehir Turkey

The vehicle routing problem with backhauls (VRPB) is an extension of the standard vehicle routing problem. VRPB has two sets of customers: linehaul customers and backhaul customers. The aim of this study is to propose a new algorithm based on fuzzy multi-objective programming (FMOP-VRPB algorithm) to solve the VRPB. The FMOP-VRPB algorithm has three phases;clustering, routing and local search. In the clustering phase, customers are assigned to vehicles by the proposed multi-objective programming (MOP) model with two objective functions: minimizing the total distance and maximizing the total savings value. The proposed MOP model is solved by fuzzy operators. The weights of the objectives are also calculated by a fuzzy two-person zero-sum game with mixed strategies using membership functions in a fuzzy pay-off matrix. In the routing phase, each vehicle is routed as a traveling salesman problem with backhauls. The local search phase is used to improve the routes. The primary contributions of the FMOP-VRPB algorithm are to consider the two objectives, to determine the weights of objectives using the proposed fuzzy pay-off matrix in the clustering phase and to use only mathematical programming in both the clustering and routing phases through many customers in an acceptable CPU time. The algorithm will also show that the proposed MOP model defines the seed customers itself in the clustering phase and will always generates feasible clusters, contrary to the reports in the literature. Benchmark problems from the literature are solved to test the performance of the FMOP-VRPB algorithm. The results indicate that the FMOP-VRPB algorithm generates sufficient solutions, and CPU times are within acceptable limits. In addition, a weekly routing problem for a logistics department of a ceramics firm in Turkey is solved by the FMOP-VRPB algorithm. Additionally, this study is the first to solve a real world VRPB;the solution shows that the FMOP-VRPB algorithm is suitable and effectiv

关键词： Vehicle routing problems with backhauls multi-objective programming Fuzzy approach Fuzzy pay-off matrix

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Sustainable fuel portfolio optimization: Integrated fuzzy multi-objective programming and multi-criteria decision making

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JOURNAL OF CLEANER PRODUCTION 2018年 176卷 304-319页

作者： Sehatpour, Mohammad-Hadi Kazemi, Aliyeh Univ Tehran Fac Management Dept Ind Management Tehran Iran

The chronic illness of transportation sector is its excessive dependence on petroleum products that necessitates immediate actions to mitigate negative externalities. Developing an environmentally benign, economically feasible, and socially acceptable fuel portfolio can generally, improve the sustainability of future transportation systems. This study aims to predict an optimal fuel portfolio based on different concerns for light-duty vehicles of Iran in the light of alternative fuels until 2025. Six potential fossil and renewable fuels including gasoline, diesel, compressed natural gas (CNG), liquid petroleum gas (LPG), a mixture of 85% ethanol and 15% gasoline (E85) and biodiesel, and one gasoline-electric hybrid technology competed through an integrated fuzzy multi-objective programming. Seven goals with environmental, cost, social and policy nature, as well as systematic constraints and fuel priority (obtained by the application of a multi-criteria decision making (MCDM) method) had to be met in the model. The solution of the model along with the sensitivity analysis of weights and aspiration levels indicated that with an acceptable possibility of achieving the goals, CNG had the greatest share in the optimal fuel portfolio followed by gasoline, LPG and diesel. Through the intended horizon, the fossil fuels' share has declined such that 13.5% of the optimal portfolio was replaced by hybrid technology, biodiesel and E85 in 2025, and more importantly, carbon dioxide emission and fuel cost could be mitigated by 11% and 18%, respectively in the same year. Two scenarios focusing on environmental and cost goals were defined through assigning 70% and 80% of the weights to the related goals, respectively;the results revealed that the main characteristics of the optimal portfolio were stable. Likewise, the analysis of the aspiration and tolerance levels of the goals proved the stability of the model and revealed that these parameters play a sensitive role in the model an

关键词： Fuel portfolio optimization Transportation alternative fuel multi-objective programming Light-duty vehicle Biofuel

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Development of a New Municipal Solid Waste Management System: multi-objective programming for a Merged Metropolis

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ENVIRONMENTAL ENGINEERING SCIENCE 2013年第4期30卷 153-160页

作者： Wu, Edward Ming-Yang Tsai, Chia-Cheng Lin, Chitsan Kuo, Shu-Lung Kang, Zhi-Bo I Shou Univ Dept Civil & Ecol Engn Kaohsiung Taiwan Natl Kaohsiung Marine Univ Dept Marine Environm Engn Kaohsiung 811 Taiwan Natl Univ Kaohsiung Gen Educ Ctr Kaohsiung Taiwan

On December 25, 2010, two administrative regions with entirely different administrative status, resources, and areas of development, Kaohsiung City and Kaohsiung County, were required by a long-term national land reform program in Taiwan to merge into one administrative entity. A new plan for managing solid wastes had to be quickly implemented to provide services of equal quality to all residents. The government of the new administrative region is required to initiate a new plan at the top level to provide a platform for planning sublevel solid waste collection and disposal systems. To address the issue, this study used an urban planning approach and multi-objective mathematical programming to reconcile conflicting objectives within the system, which must be built and maintained at minimum cost and provide maximum equity. Because the second objective of maximum equity is difficult to express quantitatively, this study initiated an indicator for this variable, that is, to minimize the total metric ton-kilometers of waste being transported. Furthermore, a constraint method was introduced to simplify the two objectives into a single objective function. Additionally, this model pioneered the inclusion of time as a variable. This made possible a time-dependent dynamic annual solution for each year of the 10-year study period. Hence, the model reflected the actual solid waste complexity in the newly merged region and provided valuable information for top-down planning of future subsystems projects.

关键词： cost minimization deterministic status modeling of equity multi-objective programming municipal solid waste management superior plan

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A multi-objective programming approach to 1.5-dimensional assortment problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期179卷 64-79页

作者： Gasimov, Rafail N. Sipahioglu, Aydin Sarac, Tugba Eskisehir Osmangazi Univ Dept Ind Engn TR-26030 Bademlik Eskisehir Turkey

In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches. (c) 2006 Elsevier B.V. All rights reserved.

关键词： cutting 1.5-dimensional assortment problem multi-objective programming weighted sum scalarization conic scalarization mixed integer linear programming

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