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A ranking algorithm for bi-objective quadratic fractional integer programming problems

OPTIMIZATION 2017年第11期66卷 1913-1929页

作者： Sharma, Vikas Dahiya, Kalpana Verma, Vanita Thapar Univ Sch Math Patiala Punjab India Panjab Univ UIET Chandigarh India Panjab Univ Dept Math Chandigarh India

An algorithm to solve bi-objective quadratic fractional integer programming problems is presented in this paper. The algorithm uses epsilon-scalarization technique and a ranking approach of the integer feasible solution to find all nondominated points. In order to avoid solving nonlinear integer programming problems during this ranking scheme, the existence of a linear or a linear fractional function is established, which acts as a lower bound on the values of first objective function of the biobjective problem over the entire feasible set Numerical examples are also presented in support of the theory.

关键词： Fractional programming multiobjective programming integer programming

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FUZZY COORDINATION OF multiobjectiveS REFLECTING THE OPERATORS INTENTION FOR DYNAMIC GENERATION RESCHEDULING

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 1992年第5期14卷 314-320页

作者： MAEKAWA, T YASUDA, K YOKOYAMA, R OHTSUKI, H MIZUKAMI, Y Department of Electric Engineering Tokyo Metropolitan University 1-1 Minami-Osawa Hachioji-City Tokyo 192-03 Japan Kansai Electric Power Co. Inc. 3-3-22 Nakanoshima Kita-ku Osaka 530 Japan

This paper proposes a novel and efficient algorithm to obtain the optimal generation dispatch reflecting the operator's intention in power system rescheduling by solving a multi-objective optimization problem. In deciding the optimal system operation, various objectives, such as economy, quality and transmission security, should be attained simultaneously. However, these objectives are contradictory to each other and are in trade-off relations, thus making it difficult to handle this class of problems by conventional approaches. In the proposed algorithm, the optimal generation dispatch problem is formulated as a multi-objective optimization problem. Fuzzy coordination technique based on fuzzy set theory is used to obtain an optimal solution. Evaluation indices composed of fuel cost, transmission line overload and AFC regulation capacity margin are measured by the membership functions, and multi-objective optimization is solved by maximizing the composite performance index, namely, the fuzzy decision-making The proposed algorithm has made it possible to treat optimal dispatch problems with multiple objectives and to grasp trade-off relations between selected indices. The effect of uncertain factors pertaining to power systems can also be taken into account. The choice of membership function parameters, reflecting the operator's preference of one of the objectives, influences the overall performance of the optimization procedure. Such an approach allows system operators to decide on different preferences according to system operating conditions, thus resulting in a more flexible operation. The validity and effectiveness of the proposed approach are verified through numerical examples on the 10 mode, 5 generator system.

关键词： FUZZY SET THEORY GENERATION CONTROL ECONOMIC DISPATCH AFC REGULATION CAPACITY LINE SECURITY multiobjective programming

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A Revised Pascoletti-Serafini Scalarization Method for multiobjective Optimization Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2018年第2期178卷 560-590页

作者： Akbari, Fereshteh Ghaznavi, Mehrdad Khorram, Esmaile Amirkabir Univ Technol Fac Math & Comp Sci Hafez Ave Tehran Iran Shahrood Univ Technol Fac Math Sci Shahrood Iran

The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti-Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti-Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti-Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples.

关键词： multiobjective programming Scalarization technique Pascoletti-Serafini method Properly efficient solution

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A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期238卷 475-496页

作者： Petridis, Konstantinos Chatzigeorgiou, Alexander Stiakakis, Emmanouil Aston Univ Aston Business Sch Birmingham B4 7ET W Midlands England Univ Macedonia Dept Appl Informat Thessaloniki 54006 Greece

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA (S-T DEA) approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a multiobjective Mixed Integer Linear programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

关键词： Data Envelopment Analysis Efficiency OR in software multiobjective programming Linear programming

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Mixed type duality for multiobjective variational problems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2000年第2期252卷 571-586页

作者： Mukherjee, RN Rao, CP Banaras Hindu Univ Inst Technol Dept Appl Math Varanasi 221005 Uttar Pradesh India

The concept of mixed-type duality has been extended to the class of multiobjective variational problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained for rho -convex (generalized rho -convex) functions. These studies have been generalized to the case of rho -invex (generalized rho -invex) functions. Our results apparently generalize a fairly large number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions. (C) 2000 Academic Press.

关键词： mixed-type dual efficient solution p-convex p-invex multiobjective programming

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A New Approach on multiobjective Higher-Order Symmetric Duality Under Cone-Invexity

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2021年第1期44卷 479-495页

作者： Verma, Khushboo Verma, Jai Prakash Ahmad, Izhar Univ Lucknow Fac Engn Dept Appl Sci & Humanities Lucknow 226031 Uttar Pradesh India Netaji Subhash Chandra Bose Govt Girls PG Coll Dept Econ Lucknow 226024 Uttar Pradesh India Univ Lucknow Lucknow Uttar Pradesh India King Fand Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, we introduce a new pair of multiobjective higher-order symmetric dual models with cone constraints. Weak, strong and converse duality theorems for a such pair are discussed under higher-order cone-invex functions. Three non-trivial examples are presented to show the uniqueness of higher-order cone-invex function and existence of the multiobjective higher-order symmetric dual model. Several known results are obtained as special cases.

关键词： Higher-order symmetric duality multiobjective programming Higher-order invexity generalized invexity Duality theorems

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SUCCESSIVE LINEAR-programming FOR RATIO GOAL PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1987年第3期32卷 426-434页

作者： ARMSTRONG, R CHARNES, A HAKSEVER, C UNIV TEXAS CTR CYBERNET STUDIESAUSTINTX 78712 BOSTON COLL SCH MANAGEMENTCHESTNUT HILLMA 02167

This paper develops two effective methods for solution of the nonlinear and non-convex programming problems of multiple ratio goal models. They are based on Charnes and Cooper's convergence theorem for an associated sequence class of linear programs. The Charnes-Cooper results are extended to develop two alternate algorithms and implementations effectively employing new information en route to solution to achieve significant savings in computation time over methods not taking advantage of such information. Possible uses for other applications than the computed examples or for other model classes are also indicated. [ABSTRACT FROM AUTHOR]

关键词： multiobjective programming non-convex programming ratio goals programming

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Formulation of an automatic lens design problem by modification of weighted Tchebycheff norm method

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OPTICAL REVIEW 1997年第6期4卷 695-699页

作者： Matsui, H Tanaka, K Canon Inc Engn Informat Syst Dev & Operat Ctr Ohta Ku Tokyo 146 Japan Canon Inc Res & Dev Headquarters Ohta Ku Tokyo 146 Japan

Automatic lens design is viewed as a multiobjective optimization problem and is resolved by a minimization of the weighted Tchebycheff norm of objective functions. It is analytically solved using the multiplier method and a solution vector is transformed into the same form as the normal equation of the least squares method. Some numerical examples are given to show the effectiveness of the proposed method. The resultant solutions can not be obtained using the damped least squares method.

关键词： automatic lens design damped least squares least squares multiobjective programming Tchebycheff norm zoom lens

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Half-open polyblock for the representation of the search region in multiobjective optimization problems: its application and computational aspects

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2021年第1期19卷 41-70页

作者： Hoai, Pham Thi Thi, Hoai An Le Nam, Nguyen Canh Hanoi Univ Sci & Technol Sch Appl Math & Informat Dept Appl Math 1 Dai Co Viet Rd Hanoi Vietnam Univ Lorraine LGIPM Dept Informat & Applicat F-57000 Metz France

The search region in multiobjective optimization problems is a part of the objective space where nondominated points could lie. It plays an important role in the generation of the nondominated set of multiobjective combinatorial optimization (MOCO) problems. In this paper, we establish the representation of the search region by half-open polyblocks (a variant concept of "polyblock" in monotonic optimization) and propose a new procedure for updating the search region. We also study the impact of stack policies to the new procedure and the existing methods that update the search region. Stack policies are then analyzed, pointing out their performance effectiveness by means of the results of rich computational experiments on finding the whole set of nondominated points of MOCO problems.

关键词： multiobjective programming multiobjective discrete programming Monotonic optimization Weighted sum scalarization e-constraint method Multi-service outsourcing problem multiobjective knapsack problem multiobjective assignment problem

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Multiple objective project portfolio selection based on reference points

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Journal of Business Economics 2016年第1-2期86卷 23-33页

作者： Stewart, Theodor J. Department of Statical Sciences University of Cape Town 7701 Rondebosch Cape Town South Africa Alliance Manchester Business School University of Manchester Manchester M15 6PB United Kingdom

The problem of selecting a portfolio of research and development projects from a set of proposed projects subject to resource constraints is formulated as a multiobjective optimization problem. Three categories of objectives are identified, namely quantitative, qualitative and balance/distributional. The first two are linear in the binary decision variables, but the third involves nonlinear measures of discrepancy between desired and actual distributions of activity amongst defined categories. The result is a nonlinear combinatorial multiobjective optimization problem. A form of reference point approach is motivated and developed as a solution method, and a special purpose genetic algorithm is implemented for obtaining the solution numerically. Extensions to interactive approaches for exploration of the efficient frontier are presented and discussed. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： multiobjective programming Project portfolios Reference point method

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