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A BOUND-IMPROVING APPROACH TO discrete programming-PROBLEMS

MATHEMATICAL programming 1994年第2期66卷 205-209页

作者： BARCIA, P COELHO, JD 1. Department of Economics Travessa Estevao Pinto Universidade Nova de Lisboa Campolide P-1000 Lisboa Portugal

This note deals with the extension of the bound-improving sequence idea to general discrete programming problems.

关键词： discrete programming LAGRANGEAN DUALITY

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Introduction of a new class of variables to discrete and integer programming problems

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ANNALS OF OPERATIONS RESEARCH 1999年 86卷 39-51页

作者： Hajian, MT Rodosek, R Richards, B Univ London Imperial Coll Sci Technol & Med William Penny Lab London SW7 2AZ England

In formulating a combinatorial optimisation problem (COP) using discrete or Integer programming (IP) modelling techniques, the modeller is restricted to use only certain predefined discrete variables and sets which are linked by sets of linear equality and inequality constraints. Definition of many COPs includes restrictions in which the use of disequality (DI) constraints in their mathematical representation is inevitable. To represent this type of constraint a number of binary variables and extra constraints are usually introduced, which lead to an increase in the size of the model in terms of variables and constraints. In this paper, we introduce a new class of discrete variables which enables the modeller to represent DI constraints more efficiently in the mathematical formulation of a combinatorial optimisation problem. We have also introduced a new branching scheme to the conventional simplex based Branch and Bound (B & B) algorithm in order to deal with this type of variables. To study the effect of these variables, we modelled and solved a set of five classic problems, first using conventional MP variables and second, exploiting the new proposed variables, and compared the results. The empirical results show a promising improvement on the performance of the B & B algorithm. The contribution of this paper is (1) the introduction of a new class of discrete variables which can help to build smaller models, and (2) new branching schemes on these variables that can improve the B & B performance.

关键词： mathematical modelling discrete programming constraint logic programming dis-equality constraints branch and bound

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REDUCING TWO-STAGE PROBABILISTIC OPTIMIZATION PROBLEMS WITH discrete DISTRIBUTION OF RANDOM DATA TO MIXED-INTEGER programming PROBLEMS

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CYBERNETICS AND SYSTEMS ANALYSIS 2014年第5期50卷 679-692页

作者： Norkin, V. I. Kibzun, A. I. Naumov, A. V. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Moscow Inst Aviat Technol Moscow Russia

We consider two-stage stochastic programming models with quantile criterion as well as models with a probabilistic constraint on the random values of the objective function of the second stage. These models allow us to formalize the requirements for the reliability and safety of the system being optimized and to optimize system's performance under extreme conditions. We propose a method of equivalent transformation of these models under discrete distribution of random parameters to mixed-integer programming problems. The number of additional integer (Boolean) variables in these problems equals to the number of possible values of the vector of random parameters. The obtained mixed optimization problems can be solved by powerful standard discrete optimization software. To illustrate the approach, the results of numerical experiment for the problem of small dimension are presented.

关键词： stochastic programming two-stage problems quantile programming probabilistic constraints deterministic equivalent mixed-integer optimization problems discrete programming

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Smart Enumeration Technology 1

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7th International Russian Automation Conference, RusAutoCon 2024

作者： Groppen, V.O. Tuayeva, I.V. 44 Nikolaev Str Vladikavkaz362021 Russia

ISBN: (数字)9783031824944

ISBN: (纸本)9783031824937

Proposed is an enumeration technology based on search of local optimum of extremal problems with discrete variables as well as numerical values of integrals, the roots of equations, and extreme values of equations for the problems with continues variables. The aim is to propose an enumeration technology for obtaining numerical solutions of acceptable quality for a wide range of problems in minimal time to find a solution. This approach includes possibility of predictive procedures usage to reduce the time of intermediate calculations, but it does not guarantee any gain in total running time, since part of this time is spent on searching for predictive dependencies. Nevertheless, it is shown that as the enumeration volume increases, the efficiency of the proposed approach also increases. It has been analytically proved and experimentally confirmed that, in comparison with the sequential search leading to the same quality of solution, the upper bound for the gain in running time for the problems with continues variables is equal to two. All descriptions of this approach are illustrated with examples and with statistical results of experimental verification of the effectiveness of this approach in relation to problems with discrete and continuous variables. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Analyze of efficiency Brute force Continuous variables discrete programming Enumeration Local optimum Predictive procedure

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Optimization of slabs using object oriented programming

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COMPUTERS & STRUCTURES 2004年第9-10期82卷 741-752页

作者： Al-Assaf, A Saffarini, HS Univ Jordan Amman 1942 Jordan

This paper discusses the application of Object-oriented programming (OOP) to the optimization of concrete slabs. This is achieved by combining: modeling, structural analysis, concrete design, cost estimation and discrete optimization together with data on cost of systems and materials. The user gets the optimal design parameters, steel topology, optimal slab system and least costs. The paper describes the overall design of the software system as well as some programming details and strategies. Inheritance and the repository model are utilized in the optimization of slabs. The unified modeling language (UML) notation is adopted. The advantages of using OOP over structured programming are discussed with particular reference to the software developed in this research. A case study on the selection of optimal system among common slab systems is briefly shown. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： optimization concrete slab structure UML object-oriented programming (OOP) discrete programming repository model

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ANALYZING AND MODELING THE MAXIMUM DIVERSITY PROBLEM BY ZERO-ONE programming

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DECISION SCIENCES 1993年第6期24卷 1171-1185页

作者： KUO, CC GLOVER, F DHIR, KS UNIV COLORADO GRAD SCH BUSINESS ADMBOULDERCO 80309

The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero-one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP-hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.

关键词： discrete programming Linear programming Mathematical programming

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COMPUTER-AIDED PROCESS STRUCTURING VIA MIXED INTEGER programming

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DECISION SCIENCES 1988年第4期19卷 750-761页

作者： KLEIN, G BECK, PO KONSYNSKI, B SO METHODIST UNIV EDWIN L COX SCH BUSINESSDALLASTX 75275 AMER AIRLINES INC DFW AIRPORTTX 75261 HARVARD SCH BUSINESS BOSTONMA 02163

Systems development managers today are working with increasingly complex systems, revealing a need for computer-aided techniques in software system definition, design, and construction. The ultimate task of the software engineer is the development of tools and procedures which reduce the effort involved in production of effective software. To be effective, software must possess characteristics of correctness, reliability, efficiency, documentation, and flexibility. This paper develops a measure for software effectiveness and a computer aid for determining process structure in program module specification. The proposed method uses various criteria and a mixed integer program to decompose a system graph into program modules. [ABSTRACT FROM AUTHOR]

关键词： Computer Applications discrete programming Management Information Systems

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Competitive acquisition of prioritizable capacity-based ancillary services

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IEEE TRANSACTIONS ON POWER SYSTEMS 2004年第1期19卷 569-576页

作者： Chicco, G Gross, G Politecn Torino Dipartimento Ingn Elettr Ind I-10129 Turin Italy Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

The rational buyer procedure provides the competitive procurement of capacity-based ancillary services (AS) in unbundled markets by the independent grid operator (IGO). The capacity-based AS are prioritized in order of ascending response times. Prioritization allows substitutability of the AS by automatically making the unused capacity of a higher priority AS usable for any lower priority AS without the need of submitting additional offers. We develop an efficient scheme for the rational buyer procedure for the acquisition of the prioritizable capacity-based AS. The scheme allows the simultaneous determination of the successful offers in the multiauction procedure through the effective deployment of discrete programming notions and the exploitation of the structural characteristics of the formulation. A key feature is the incorporation of physical constraints such as capacity, ramp-rate, and interzonal constraints. The use of bounding techniques combined with procedures for the quick detection of infeasible combinations of the offer prices and the identification of avoidable calculations leads to reducing the computational burden. The effectiveness and computational efficiency of the scheme are illustrated with representative numerical results including case studies based on the IEEE 118-bus network.

关键词： ancillary service provision discrete programming independent grid operator prioritizable capacity-based services ramp-rate constraints rational buyer simultaneous auctions

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Theoretical and algorithmic results for a class of hierarchical fleet mix problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第3期198卷 741-747页

作者： Cambini, Riccardo Riccardi, Rossana Univ Pisa Dept Stat & Appl Math Fac Econ I-56124 Pisa Italy

In this paper a workforce model is studied from both a theoretical and an algorithmic point of view. In the considered hierarchical model workforce units can be substituted by higher qualified ones;external workforce can also be hired to cover low qualified jobs. An exact recursive solution algorithm is proposed to solve the problems and its efficiency is improved by means of cut conditions and discrete convexity properties. Finally, the results of a computational test are provided. (C) 2008 Elsevier B.V. All rights reserved.

关键词： discrete programming discrete convexity Optimal fleet mix

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AN OPTIMAL METHOD FOR A DETERMINISTIC JOINT REPLENISHMENT INVENTORY POLICY IN discrete-TIME

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1995年第5期46卷 649-657页

作者： KLEIN, CM VENTURA, JA PENN STATE UNIV UNIVERSITY PKPA 16802

In this paper we derive an optimal solution to the multi-item single-supplier inventory problem with two types of set-up costs. In the case considered, replenishment opportunities are restricted to the beginning of th... 详细信息

关键词： INVENTORY MULTIITEM discrete programming

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