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Using multiobjective optimization to map the entropy region

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期63卷 45-67页

作者： Csirmaz, Laszlo Cent European Univ Budapest Hungary Renyi Inst Budapest Hungary

Mapping the structure of the entropy region of at least four jointly distributed random variables is an important open problem. Even partial knowledge about this region has far reaching consequences in other areas in mathematics, like information theory, cryptography, probability theory and combinatorics. Presently, the only known method of exploring the entropy region is, or equivalent to, the one of Zhang and Yeung from 1998. Using some non-trivial properties of the entropy function, their method is transformed to solving high dimensional linear multiobjective optimization problems. Benson's outer approximation algorithm is a fundamental tool for solving such optimization problems. An improved version of Benson's algorithm is presented, which requires solving one scalar linear program in each iteration rather than two or three as in previous versions. During the algorithm design, special care is taken for numerical stability. The implemented algorithm is used to verify previous statements about the entropy region, as well as to explore it further. Experimental results demonstrate the viability of the improved Benson's algorithm for determining the extremal set of medium-sized numerically ill-posed optimization problems. With larger problem sizes, two limitations of Benson's algorithm is observed: the inefficiency of the scalar LP solver, and the unexpectedly large number of intermediate vertices.

关键词： multiobjective programming Effective solutions Entropy region Benson's algorithm Entropy inequality

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A bi-objective ergonomic assembly line balancing model with conic scalarization method

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HUMAN FACTORS AND ERGONOMICS IN MANUFACTURING & SERVICE INDUSTRIES 2022年第6期32卷 494-507页

作者： Yetkin, Busra N. Kahya, Emin Eskisehir Osmangazi Univ Dept Ind Engn M3 BlokMesel Yerleskesi TR-26480 Eskisehir Turkey

The most important factor affecting efficiency and ergonomic risk levels in an assembly line design is the problem of assigning certain tasks to certain stations, namely the assembly line balancing problem. In the literature, assembly line balancing problem has often been studied, but studies that consider ergonomic risks are deficient. Recently, it has been one of the issues that have started to attract great attention with the realization of health problems caused by assembly lines. To this end, in this study, a bi-objective mathematical model is developed that considers balancing assembly line station time and ergonomic risk levels, simultaneously. It is aimed to minimize both station time and the total deviations of ergonomic risk scores for the stations. Weighted sum and conic scalarization methods are applied to solve the bi-objective model. To analyze the outcomes of the developed model, an application is proposed and tested on a real industrial case, at a home appliance assembly line. The deployment of the OMAX method is a contribution to the literature since it shows an analysis tool which evaluates the results of assembly line balancing. This method evaluates the performance of the stations based on different criteria such as station time and ergonomic risk. The number of high-risk stations is obtained as 13 in the single-objective model aiming to minimize the station time, while it is found to be nine in the bi-objective model solved with CSM, without an increase in the total number of stations.

关键词： assembly line balancing conic scalarization ergonomic risk evaluation multiobjective programming REBA

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multiobjective duality using Fritz John conditions

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 1998年第1期15卷 63-74页

作者： Gulati, TR Ahmad, I Univ Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

A Mond-Weir type dual is formulated for a multiobjective fractional programming problem and duality theorems are established that relate to efficient solutions of the primal and dual problems. The strong and converse duality theorems are proved using Fritz John type necessary conditions, which avoid the need of a constrain qualification.

关键词： multiobjective programming fractional programming efficiency duality generalized convexity

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Life-cycle assessment and production policy: An application to corrugated paperboard manufacture

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2000年第2期59卷 157-165页

作者： Lee, YM Ding, CY Natl Taiwan Univ Inst Nat Resource Management Taipei 10433 Taiwan Ind Technol Res Inst 321 Union Chem Labs Hsinchu 300 Taiwan

The aim of the study is to develop a framework of applying life cycle assessment to production policy. A case-study on corrugated paperboard manufacture is therefore implemented. The application framework comprises three components: the conventional life cycle assessment procedure, the analytical hierarchy process, and a multiobjective programming model. In the decision model for production policy adjustment the objectives of cost-effectiveness and environment-friendliness are incorporated The environmental impacts are classified as categories of pollution and disturbance as well as space groups of global, regional and local scales. This makes applicable the analytical hierarchy process for evaluating the environmental impacts. In the application the objectives incorporated are found to be competitive. The manufacture has to trade the increase of production costs for the reduction of environmental impacts. We also observe that the marginal effects of impacts on cost increase as the spatial scales of impact increase. (C) 2000 Academic Press.

关键词： life-cycle assessment analytical hierarchy process multiobjective programming corrugated paperboard

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The controlled estimation method in the multiobjective linear fractional problem

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COMPUTERS & OPERATIONS RESEARCH 2004年第11期31卷 1821-1832页

作者： Caballero, R Hernández, M Univ Malaga Dept Appl Econ E-29071 Malaga Spain

This paper introduces a new method to estimate the weakly efficient set for the multiobjective Linear Fractional programming problem. The main idea is based on the procedure proposed by Tzeng and Hsu (In: G.H. Tzeng, H.F. Wang, U.P. Wen, L. Yu (Eds.), Multiple Criteria Decision Making, Springer, New York, 1994, pp. 459-470), called CONNISE. However, as we will explain in this paper, the CONNISE method is not always convergent for problems with more than two objectives. For this reason, we have developed a new method, called "The Controlled Estimation Method", based on the same concept as CONNISE regarding the decision-maker being able to control distances between points from the estimation set he/she wants to find, while ensuring the method is convergent with problems with more than two objectives. Thus, we propose an algorithm able to calculate a discrete estimation of the weakly efficient set that verifies this property of the CONNISE method, but further, improves it thanks to its convergence and the fact that it satisfies the three good properties suggested by Sayin (Math. programming 87(3) (2000) 543): Coverage, Uniformity, and Cardinality. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming fractional programming

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Resource Conflicts Resolution of Sophisticated Production Lines During the Process of Product Renewal

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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 2024年 71卷 5965-5981页

作者： Liu, Yong Wang, Zhaoting Huang, Zihong Forrest, Jeffrey Yi-Lin Jiangnan Univ Sch Business Wuxi 214122 Peoples R China Slippery Rock Univ Penn Sch Business Slippery Rock PA 16057 USA

There exist a variety of resource conflicts due to resource constraints in production lines during the period of renewal of sophisticated products manufacturing, probably leading to production delays and resource wastage. With respect to the resource conflicts of the resource-constrained multiproject scheduling problem in sophisticated product lines, we construct a multiproject production line resource conflict resolution model, design a feedback regulation, and a hybrid genetic algorithm based on the cooperative game negotiation mechanism, which covers four stages starting from the manufacturer receiving the orders of original and upgraded products, taking into account of resource reallocation, resource sharing, and seeking help from emergency suppliers, to respond highly to the dynamics of customer orders and optimize production systems, achieving intelligent advances. The case results show that the proposed method can save up to 77.84% of the delay and scheduling cost, and these savings can allow the manufacturer to increase profits by 10.82% due to shortening the production delay. The current work not only helps manufacturers of sophisticated products to improve their production efficiencies and reduce delay cost but also provides a certain basis for future managers to make production management decisions.

关键词： Production Job shop scheduling Manufacturing Delays Costs Resource management Business Conflicts and scheduling feedback regulation limited resources multiobjective programming multiproject production

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Constraint approach to performance-based design of steel moment-resisting frames

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ENGINEERING STRUCTURES 2007年第2期29卷 186-194页

作者： Pan, Peng Ohsaki, Makoto Kinoshita, Takuya Kyoto Univ Dept Architecture & Architectural Engn Kyoto 6158540 Japan

An optimization method is proposed for performance-based design of steel moment-resisting frames. The multiple design requirements or targets are incorporated into a multiobjective programming problem, where a new formulation based on the constraint approach is presented for obtaining trade-off solutions. The maximum interstory drift angles against seismic motions of three levels are considered as hard targets that should be strictly constrained in the optimization problem. The maximum floor acceleration and total structural volume are conceived as soft targets that are incorporated as objective functions of the multiobjective programming problem. The proposed constraint approach is applied to two representative steel moment-resisting frames, and the characteristics of their optimal designs considering multiple design targets are investigated. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： steel moment-resisting frame performance-based design seismic response multiobjective programming constraint approach

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Interactive multiobjective optimization approach to the input-output design of opening new branches

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 530-538页

作者： Park, K. Sam Shin, Dong Eun Korea Univ Sch Business Seoul 136701 South Korea

We demonstrate a real-world application of the interactive multiple objective optimization (MOO) approach to the simultaneous setting of input and output amounts for the opening of new branches. As illustrated by the case example, all the branches of a fast-food company employ multiple inputs to generate multiple outputs. The company launches several new branches each year and, therefore, needs to plan the quantities of inputs and outputs to be used and produced before their operations. Such input-output settings are a vital practical problem that arises whenever a new branch is opened in a host of different industries. In this paper, we show in detail the entire process of the application from modeling the case problem to generating its solution. In the modeling stage, a data envelopment analysis model and a statistical method are subsequently utilized to form a nonlinear MOO problem for the input-output settings. To solve this problem, we then develop and apply an interactive MOO method, which combines the two earlier interactive methods (Geoffrion et al., 1972;Zionts and Wallenius, 1976), while compensating for their drawbacks and capturing their positive aspects. (C) 2012 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Interactive approach Nonlinear programming Data envelopment analysis Input-output design New branches

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multiobjective nonlinear second order symmetric duality with (K,F)-pseudoconvexity

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APPLIED MATHEMATICS AND COMPUTATION 2012年第4期219卷 2142-2148页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

The purpose of this paper is to introduce a new class of generalized cone-pseudoconvex functions and strongly cone-pseudoconvex functions, called second order (K,F)-pseudoconvex functions and strongly second order (K,F)-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated over arbitrary generalized cone-pseudoconvex functions. For these second order symmetric dual programs, the weak, strong and converse duality theorems are established using the above generalization of cone-pseudoconvex functions. A self duality theorem is also given by assuming the functions involved to be skew-symmetric. (C) 2012 Elsevier Inc. All rights reserved.

关键词： multiobjective programming Second-order symmetric dual models Duality theorems Pseudoconvex functions Cones

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A reduced Jacobian method with full convergence property

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OPTIMIZATION LETTERS 2024年第7期18卷 1647-1671页

作者： El Maghri, M. Elboulqe, Y. Hassan II Univ Dept Math & Comp Fac Sci Ain Chock BP 5366 Casablanca Morocco

In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe (J Optim Theory Appl 179:917-943, 2018) for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant possesses the full convergence property in the sense that the entire sequence converges whenever the objectives are quasiconvex. Simulations are reported showing the performance of this variant compared to RJM and the nondominated sorting genetic algorithm (NSGA-II).

关键词： Muticriteria optimization Pareto efficiency multiobjective programming Reduced gradient method multiobjective descent direction Convergence analysis

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