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Bi-objective optimisation over a set of convex sub-problems

ANNALS OF OPERATIONS RESEARCH 2022年第2期319卷 1507-1532页

作者： Cabrera-Guerrero, Guillermo Ehrgott, Matthias Mason, Andrew J. Raith, Andrea Pontificia Univ Catolica Valparaiso Valparaiso Chile Univ Lancaster Lancaster England Univ Auckland Auckland New Zealand

During the last decades, research in multi-objective optimisation has seen considerable growth. However, this activity has been focused on linear, non-linear, and combinatorial optimisation with multiple objectives. Multi-objective mixed integer (linear or non-linear) programming has received considerably less attention. In this paper we propose an algorithm to compute a finite set of non-dominated points/efficient solutions of a bi-objective mixed binary optimisation problems for which the sub-problems obtained when fixing the binary variables are convex, and there is a finite set of feasible binary variable vectors. Our method uses bound sets and exploits the convexity property of the sub-problems to find a set of efficient solutions for the main problem. Our algorithm creates and iteratively updates bounds for each vector in the set of feasible binary variable vectors, and uses these bounds to guarantee that a set of exact non-dominated points is generated. For instances where the set of feasible binary variable vectors is too large to generate such provably optimal solutions within a reasonable time, our approach can be used as a matheuristic by heuristically selecting a promising subset of binary variable vectors to explore. This investigation is motivated by the problem of beam angle optimisation arising in radiation therapy planning, which we solve heuristically to provide numerical results.

关键词： multiple objective programming Convex optimisation Mixed binary programming Intensity modulated radiation therapy

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A MULTIobjective programming FRAMEWORK FOR INTEGRATING TIMBER AND WILDLIFE MANAGEMENT

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ENVIRONMENTAL MANAGEMENT 1988年第2期12卷 163-171页

作者： MENDOZA, GA 1. Department of Forestry University of Illinois 110 Mumford Hall 1301 West Gregory St. 61801 Urbana IL USA

This article describes a multiobjective programming (MOP) framework for integrating timber and wildlife management. The framework allows for the simultaneous consideration of timber and wildlife objectives. Management strategies are defined in terms of management regimes consisting of a time-identified and site-specific schedule of activities. A MOP model is described and demonstrated using an integrated planning example involving a forest managed for timber production and a variety of wildlife species.

关键词： multiple-use forestry multiple objective programming

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Interactive bicriterion decision support for a large scale industrial scheduling system

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ANNALS OF OPERATIONS RESEARCH 2015年第1期227卷 45-61页

作者： Makarouni, Ioanna Psarras, John Siskos, Eleftherios Natl Tech Univ Athens Sch Elect & Comp Engn Decis Support Syst Lab Athens Greece

In this paper we develop an interactive decision analysis approach to treat a large scale bicriterion integer programming problem, addressing a real world assembly line scheduling problem of a manufacturing company. This company receives periodically a set of orders for the production of specific items (jobs) through a number of specialised production (assembly) lines. The paper presents a non compensatory approach based on an interactive implementation of the epsilon-constraint method that enables the decision maker to achieve a satisfactory goal for each objective separately. In fact, the method generates and evaluates a large number of non dominated solutions that constitute a representative sample of the criteria ranges. The experience with a specific numerical example shows the efficiency and usefulness of the proposed model in solving large scale bicriterion industrial integer programming problems, highlighting at the same time the modelling limitations.

关键词： multiple objective programming Interactive decision analysis Job scheduling Pareto optimality Mixed-model assembly line

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Designing communication networks for distributed control agents

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第3期153卷 544-563页

作者： Camponogara, E Talukdar, S Univ Fed Santa Catarina Dept Automacao & Sist BR-88040900 Florianopolis SC Brazil Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA

This paper is concerned with a bicriteria combinatorial optimization Problem and its applications to the design of communication networks for distributed controllers. In a bipartite graph, a subset of the edges yields a communication network for which we pay a price but, on the other hand, it induces another network that encompasses the former and for which we receive a reward. The problem is then to find the efficient solutions. The paper delivers an IP formulation for the problem of finding supported solutions, which is shown to be NP-Hard, along with families of strong valid inequalities, which are shown to draw the LP bounds closer to the Pareto optimal frontier. To approximate the frontier, heuristics are integrated in a problem-solving architecture called asynchronous team and then put to the test in two prototypical scenarios. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple objective programming multiagent systems combinatorial optimization metaheuristics

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The multiscenario lot size problem with concave costs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期156卷 162-182页

作者： Gutiérrez, J Puerto, J Sicilia, J Univ La Laguna Dept Estadist Invest Operat & Computac San Cristobal la Laguna 38271 Spain Univ Seville Dept Estadist & Invest Operat Seville Spain

The dynamic single-facility single-item lot size problem is addressed. The finite planning horizon is divided into several time periods. Although the total demand is assumed to be a fixed value, the distribution of this demand among the different periods is unknown. Therefore, for each period the demand can be chosen from a discrete set of values. For this reason, all the combinations of the demand vector yield a set of different scenarios. Moreover, we assume that the production/reorder and holding cost vectors can vary from one scenario to another. For each scenario, we consider as the objective function the sum of the production/reorder and the holding costs. The problem consists of determining all the Pareto-optimal or non-dominated production plans with respect to all scenarios. We propose a solution method based on a multiobjective branch and bound approach. Depending on whether shortages are considered or not, different upper bound sets are provided. Computational results on several randomly generated problems are reported. (C) 2003 Elsevier B.V. All rights reserved.

关键词： scenarios inventory multiple objective programming

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A bicriteria knapsack program for planning remediation of contaminated lightstation sites

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第2期140卷 427-433页

作者： Jenkins, L Royal Mil Coll Canada Dept Business Adm Kingston ON K7K 7B4 Canada

The Coastguard manages over 40 lighthouse sites on the West Coast of Canada. All of these have some ground contamination from lighthouse activities or other earlier uses of the location, such as military fortification. Now the federal government is requiring its departments to identify all pollution on land that it owns or leases, and develop an environmental management plan for contaminated sites. The author has worked with the Canadian Coast Guard, Pacific Region (CCG-PR) to develop a set of environmental criteria for prioritizing management and remediation at the lighthouse sites. The next step is to apply these criteria to determine the best action to take once preliminary environmental assessments of the sites have been completed. Two criteria dominate the immediate next actions at a site. One is the Canadian Council of Ministers of the Environment (CCME) Score, which is a measure of estimated environmental risk, and would be reduced by some immediate remediation. The other is Uncertainty, which estimates the incompleteness of the preliminary assessment and would be reduced by further testing. Working with these two criteria and a limited budget, deciding the best next step can be formulated as a bicriterion 0-1 knapsack problem. A comprehensive solution of the problem would require a parametric analysis over all possible relative weights of the two criteria, and also a parametric analysis for the budget. An exact solution would require much computation, and such a solution process could not easily be handed over to CCG-PR personnel. However, if the integer requirement in the formulation is relaxed, the problem becomes simply a matter of ranking projects by their best benefit/cost ratio, and selecting projects down the list until all the budget is allocated. This is the solution approach used here, and which is being passed to CCG-PR headquarters for their continued use. The paper illustrates the method with some disguised data from the actual CCG-PR studies. (

关键词： environment multiple objective programming knapsack problem

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AN APPROACH TO USING THE ANALYTIC HIERARCHY PROCESS FOR SOLVING multiple CRITERIA DECISION-MAKING PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第3期76卷 440-454页

作者： BRYSON, N MOBOLURIN, A HOWARD UNIV SCH BUSINESS2600 67TH ST NWWASHINGTONDC 20059 USA

In this paper we present a procedure for solving multiple criteria decision making problems. Our procedure, which is an extension of the Analytic Hierarchy Process, addresses the issue of fuzziness in the weighing information provided by the decision maker, the consequent stability of the AHP ranking of the alternatives and the sensitivity of such rankings to small perturbations. These issues are especially important when the concept of optimality incorporates parameters or weights that reflect subjective preferences. The procedure provides a consistent and systematic method for carrying out goal-seeking sensitivity analysis that captures the decision maker's preference structure using his/her indifference region.

关键词： multiple CRITERIA DECISION MAKING multiple objective programming ANALYTIC HIERARCHY PROCESS

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NONLINEAR MAPPINGS ASSOCIATED WITH THE GENERALIZED LINEAR COMPLEMENTARITY-PROBLEM

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MATHEMATICAL programming 1995年第2期69卷 255-268页

作者： EBIEFUNG, A Department of Mathematics University of Tennessee at Chattanooga Chattanooga USA

We show that the Cottle-Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.

关键词： GENERALIZED LINEAR COMPLEMENTARITY PROBLEM PIECEWISE LINEAR SYSTEMS multiple objective programming VARIATIONAL INEQUALITIES NP-COMPLETE

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Strictly feasible solutions and strict complementarity in multiple objective linear optimization

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2017年第3期15卷 303-326页

作者： Mahdavi-Amiri, N. Salehi Sadaghiani, F. Sharif Univ Technol Fac Math Sci Tehran Iran

Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established. Here, we use these results to prove some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are established. We show that primal-dual (weakly) efficient solutions satisfying strictly complementary conditions exist. Furthermore, we consider Isermann's and Kolumban's dual problems and establish conditions for the existence of strictly primal and dual feasible points. We show the existence of primal-dual feasible points satisfying strictly complementary conditions for Isermann's dual problem. Also, we give an alternative proof to establish necessary conditions for weakly efficient solutions of multiple objective programs, assuming the Kuhn-Tucker (KT) constraint qualification. We also provide a new condition to ensure the KT constraint qualification.

关键词： multiple objective programming Duality Strictly complementary conditions Strictly feasible points Farkas' lemma Primal-dual weakly efficient solutions Constraint qualification

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Multicriteria interpretability driven deep learning

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ANNALS OF OPERATIONS RESEARCH 2022年第2期346卷 1621-1635页

作者： Repetto, Marco Siemens Italy Digital Ind Milan Italy Univ Milano Bicocca Dept Econ Management & Stat Milan Italy

Deep Learning methods are well-known for their abilities, but their interpretability keeps them out of high-stakes situations. This difficulty is addressed by recent model-agnostic methods that provide explanations after the training process. As a result, the current guidelines' requirement for "interpretability from the start" is not met. As a result, such methods are only useful as a sanity check after the model has been trained. In an abstract scenario, "interpretability from the start" implies imposing a set of soft constraints on the model's behavior by infusing knowledge and eliminating any biases. By inserting knowledge into the objective function, we present a Multicriteria technique that allows us to control the feature effects on the model's output. To accommodate for more complex effects and local lack of information, we enhance the method by integrating particular knowledge functions. As a result, a Deep Learning training process that is both interpretable and compliant with modern legislation has been developed. Our technique develops performant yet robust models capable of overcoming biases resulting from data scarcity, according to a practical empirical example based on credit risk.

关键词： Artificial intelligence Machine learning Deep learning multiple objective programming Multicriteria optimization

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