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Stability analysis of efficient solutions in multiobjective integer programming:: A case study in load management

COMPUTERS & OPERATIONS RESEARCH 2008年第1期35卷 186-197页

作者： Alves, Maria Joao Climaco, Joao Antunes, Carlos Henggeler Jorge, Humberto Martins, Antonio G. Univ Coimbra Fac Econ P-3004512 Coimbra Portugal Univ Coimbra Dept Elect Engn & Comp P-3030290 Coimbra Portugal INESC Coimbra P-3000037 Coimbra Portugal

This paper presents a multiobjective linear integer programming model for supporting the choice of remote load control strategies in electric distribution network management. The model takes into account the main concerns in load management, considering three objective functions: minimization of the peak demand as perceived by the distribution network dispatch center, maximization of the utility profit associated with the energy services delivered by the controlled loads and minimization of the discomfort caused to consumers. The problem was analyzed using an interactive reference point method for multiobjective integer (and mixed-integer) linear programming. This approach exploits the use of the branch-and-bound algorithm for solving the reference point scalarizing programs through which efficient solutions are computed. Post-optimality techniques enable a stability analysis of the efficient solutions by means of computing and displaying graphically sets of reference points that correspond to the same solution. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： multiobjective integer programming interactive methods energy management

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Solution approaches for equitable multiobjective integer programming problems

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 967-995页

作者： Bashir, Bashir Karsu, Ozlem Bilkent Univ Dept Ind Engn Ankara Turkey

We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably nondominated solutions. We discuss two algorithms for finding good subsets of equitably nondominated solutions. The first approach is an extension of an interactive approach developed for finding the most preferred nondominated solution when the utility function is assumed to be quasiconcave. We find the most preferred equitably nondominated solution when the utility function is assumed to be symmetric quasiconcave. In the second approach we generate an evenly distributed subset of the set of equitably nondominated solutions to be considered further by the DM. We show the computational feasibility of the two algorithms on equitable multi-objective knapsack problem, in which projects in different categories are to be funded subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms.

关键词： Equitable preferences Equitable efficiency Equitable dominance Generalized Lorenz dominance Multi-objective knapsack problem Convex cones Fairness multiobjective integer programming Interactive algorithm

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Split algorithms for multiobjective integer programming problems

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COMPUTERS & OPERATIONS RESEARCH 2022年 140卷 1页

作者： Karsu, Ozlem Ulus, Firdevs Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey

We consider split algorithms that partition the objective function space into - 1 dimensional regions so as to search for nondominated points of multiobjective integer programming problems, where is the number of objectives. We provide a unified approach that allows different split strategies to be used within the same algorithmic framework with minimum change. We also suggest an effective way of making use of the information on subregions when setting the parameters of the scalarization problems used in the -split structure. We compare the performances of variants of these algorithms both as exact algorithms and as solution approaches under time restriction, considering the fact that finding the whole set may be computationally infeasible or undesirable in practice. We demonstrate through computational experiments that while the (-1)-split structure is superior in terms of overall computational time, the-split structure provides significant advantage under time/cardinality limited settings in terms of representativeness, especially with adaptive parameter setting and/or a suitably chosen order for regions to be explored.

关键词： multiobjective discrete optimization multiobjective integer programming Pascoletti-Serafini scalarization Weighted sum scalarization Epsilon constraint scalarization

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An Interactive Fuzzy Satisficing Method for Random Fuzzy multiobjective integer programming Problems through Probability Maximization with Possibility

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FUZZY INFORMATION AND ENGINEERING 2013年第3期5卷 335-350页

作者： Sakawa, M. Matsui, T. Katagiri, H. Hiroshima Univ Fac Engn Hiroshima 7398527 Japan

This paper considers multiobjective integer programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed by incorporating the concept of probability maximization into a possibilistic programming model. For solving transformed deterministic problems, genetic algorithms with double strings for nonlinear integer programming problems are introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution to a decision maker by updating the reference probability levels. An illustrative numerical example is provided to clarify the proposed method.

关键词： multiobjective integer programming Random fuzzy programming Possibility Probability maximization Interactive method

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multiobjective 0-1 integer programming for the use of sugarcane residual biomass in energy cogeneration

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2011年第5期18卷 605-615页

作者： Florentino, Helenice De Oliveira De Lima, Adriano Dawison De Carvalho, Lidia Raquel Balbo, Antonio Roberto Donadon Homem, Thiago Pedro UNESP Inst Biociencias Dept Bioestat Botucatu SP Brazil UNESP FCA Programa Pos Grad Energia Agr BR-18603970 Botucatu SP Brazil UNESP Fac Ciencias Dept Matemat Bauru SP Brazil UNESP FEB Programa Pos Grad Engn Eletr Bauru SP Brazil

It is well known that Brazil is the largest producer of sugarcane in the world. Nevertheless, a great concern exists about the crop system used, because the most common practice is manual harvesting with prior straw burning. The Brazilian authorities have approved a law prohibiting the burning of sugarcane crop residue before harvesting. However, mechanized harvesting creates the new problem of having to deal with the residue. Many studies have indeed proposed the use of this residue as an energy source. A major difficulty in using this residue is how to economically transport sugarcane harvest biomass from a farm to a processing centre. Besides transport costs, another concern is knowing whether the energy generated by the straw offsets the energy used, in terms of fuel, in the process. This study proposes a multiobjective integer linear programming optimization model to choose sugarcane varieties so as to minimize costs in the use of crop residue and simultaneously maximize the energy balance in such a process. Computational results are presented and discussed.

关键词： sugarcane crop residue multiobjective integer programming

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Leveraging Multicriteria integer programming Optimization for Effective Team Formation

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IEEE TRANSACTIONS ON LEARNING TECHNOLOGIES 2025年 18卷 72-84页

作者： Singh, Pallavi Huynh, Phat K. Nguyen, Dang Le, Trung Q. Moreno, Wilfrido Univ S Florida Dept Elect Engn Tampa FL 33620 USA Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA Corrigan Minehan Heart Ctr Boston MA 02114 USA Univ S Florida Dept Med Engn Tampa FL 33620 USA

In organizational and academic settings, the strategic formation of teams is paramount, necessitating an approach that transcends conventional methodologies. This study introduces a novel application of multicriteria integer programming (MCIP), which simultaneously accommodates multiple criteria, thereby innovatively addressing the complex task of team formation. Unlike traditional single-objective optimization methods, our research designs a comprehensive framework capable of modeling a wide array of factors, including skill levels, backgrounds, and personality traits. The objective function of this framework is optimized to maximize within-team diversity while minimizing both conflict levels and variance in diversity between teams. Central to our approach is a two-stage optimization process. Initially, it segments the population into subgroups using a weighted heterogeneous multivariate K-means algorithm, allowing for a targeted and nuanced team assembly. This is followed by the application of a surrogate optimization technique within these subgroups, efficiently navigating the complexities of MCIP for large-scale applications. Our approach is further enhanced by the inclusion of explicit constraints such as potential interpersonal conflicts, a factor often overlooked in previous studies. The results from our study demonstrate the optimality and robustness of our model across simulation scenarios with different data heterogeneity levels. The contributions of this study are manifold, addressing critical gaps in the existing literature with a theory-backed, empirically validated framework for advanced team formation. Beyond theoretical implications, our work provides a practical guide for implementing conflict-aware, sophisticated team formation strategies in real-world scenarios. This advancement paves the way for future research to explore and enhance this model, providing more sophisticated and efficient team formation strategies.

关键词： Task analysis integer programming Complexity theory Heuristic algorithms Data models Statistics Sociology multiobjective integer programming optimization methods team formation problem (TFP) team-based learning (TBL)

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A lexicographic approach to bi-objective loading of a flexible assembly system

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1998年第3期107卷 656-668页

作者： Sawik, T Stanislaw Staszic Univ Min & Met Fac Management Dept Comp Integrated Mfg PL-30059 Krakow Poland

The paper presents a bi-objective integer program and an approximative lexicographic approach for a bicriterion loading and routing problem in a flexible assembly system. The problem objective is to determine an allocation of tasks among the assembly stations for a set of products so as to balance station workloads and minimize total interstation transfer time. In the approach proposed, first the station workloads are balanced using a linear relaxation-based heuristic and then assembly routes are selected based on a network flow model. An illustrative example is provided and some results of computational experiments are reported. (C) 1998 Elsevier Science B.V.

关键词： flexible manufacturing system loading and routing multiobjective integer programming Lexicographic approach LP-based heuristic

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An interactive approach to bicriterion loading of a flexible assembly system

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MATHEMATICAL AND COMPUTER MODELLING 1997年第6期25卷 71-83页

作者： Sawik, TJ Department of Computer Integrated Manufacturing University of Mining & Metallurgy Faculty of Management Al. Mickiewicza 30 30-059 Krakow Poland

This paper presents integer programming formulations and an interactive solution procedure for a bicriterion loading problem in a flexible assembly system. The system is made up of a set of assembly stations linked with an automated material handling system. In the system, several different product types can be assembled simultaneously. The problem objective is to assign assembly tasks and products to stations with limited working space, so as to balance the station workloads and to minimize station-to-station product transfer time, subject to precedence relations among the tasks for a mix of product types. The solution procedure proposed is based on the weighting method and the interactive search for a set of weights which would produce the most preferred nondominated solution. Numerical examples are included to illustrate possible applications of the interactive approach for various problem formulations proposed.

关键词： flexible assembly systems production planning multiobjective integer programming

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Decomposition of loosely coupled integer programs: a multiobjective perspective

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MATHEMATICAL programming 2022年第1-2期196卷 427-477页

作者： Bodur, Merve Ahmed, Shabbir Boland, Natashia Nemhauser, George L. Univ Toronto Dept Mech & Ind Engn Toronto ON Canada Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

We consider integer programming (IP) problems consisting of (possibly a large number of) subsystems and a small number of coupling constraints that link variables from different subsystems. Such problems are called loosely coupled or nearly decomposable. In this paper, we exploit the idea of resource-directive decomposition to reformulate the problem so that it can be decomposed into a resource-directive master problem and a set of multiobjective programming subproblems. Recent methods developed for solving multiobjective problems enable us to formulate a relaxation of the master problem that is an IP whose solution yields a dual bound on the value of the original IP. This perspective provides a new, general framework for IP decomposition, in which many alternative algorithm designs are possible. Here, we develop one such algorithm, and demonstrate its viability and potential benefits with the aid of computational experiments knapsack-based instances with up to five coupling constraints and 7500 variables, comparing it with both a standard IP solver and a generic branch-and-price solver.

关键词： integer programming Resource-directive decomposition multiobjective integer programming Column generation

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Designing sustainable diet plans by solving triobjective integer programs

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2024年第3期100卷 703-721页

作者： Benvenuti, Luca De Santis, Alberto De Santis, Marianna Patria, Daniele Sapienza Univ Rome Dept Comp Control & Management Engn Via Ariosto 25 I-00185 Rome Italy Univ Florence Dept Informat Engn Via Santa Marta 3 I-50139 Florence Italy

We present an algorithm for triobjective nonlinear integer programs that combines the epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then used to determine the nondominated solutions of triobjective 0-1 models, built to design nutritionally adequate and healthy diet plans, minimizing their environmental impact. The diet plans refer to menus for school cafeterias and we consider the carbon, water and nitrogen footprints as conflicting objectives to be minimized. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. Results obtained on two models and on real world data are reported and discussed.

关键词： multiobjective integer programming Criterion space algorithm Environmental sustainability

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