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Multiple objective programming and goal programming: New trends and applications
European Journal of Operational Research 177 (2007) 1520–1522 www.elsevier.com/locate/ejor
Editorial
Multiple objective programming and goal programming: New trends and applications
Multiple Objective Programming and Goal Programming (MOPGP) is a well-established area within the field of operational research. Being able to consider conflicting objectives enables the modeling many more problems in business, economics, and engineering. In the MOPGP paradigm, the decision aspects of the issues concerned are taken into account even during the solution steps, that is, the decision maker (DM) is at least as important as the modeler. Most multiobjective techniques and concepts have been developed over the past 30 years to deal with the huge variety of complex problems that can be solved by effecting trade-offs among conflicting interests. The types of problems addressed by MOPGP can be classified as to whether they are deterministic or non-deterministic, static or dynamic, continuous or discrete, linear or non-linear, etc. The generation of the Pareto set for convex problems has in general been well addressed. Sensitivity analysis and duality have been considered and studied with reference to multiobjective problems. Many interactive methods have been proposed and utilized to address real-life situations. For the combinatorial case, exact and heuristic methods have been developed to generate or approximate the Pareto set for many classical problems, such as the traveling salesman problem, the knapsack problem, and various scheduling problems. Meanwhile, a variety of goal programming techniques have been proposed and utilized. Goal pro-
gramming, along with its many variants, can now be considered as one of the most effective strategies for solving multiobjective optimization problems. Yet, for all the progress that has been achieved, many problems remain unresolved. To date, we are still unable to generate the entire Pareto set in many cases. Multiobjective stochastic optimization problems need more study. Formulations of multiobjective game problems are not complete. We do not know how to solve dynamic multiobjective problems. For all these cases, two main questions must be answered: what kind of solutions are we looking for and how to find these solutions? This Feature Cluster of EJOR contains a set of refereed papers selected from those presented at the 6th International Conference on Multiple Objective Programming and Goal Programming: New Trends and Applications (MOPGP’04. http://mopgp04.cjb.cc/), held in the village of Hammamet, Tunisia from 4th to 6th of April 2004. The Conference was attended by over 100 participants from 18 countries. In all, 46 papers were submitted for publication out of which 22 have been accepted for the Feature Cluster.
1. Content Some of the accepted papers focus on new trends in MOPGP. By new trends we mean aspects of MOPGP that have not been extensively addressed,
0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.12.023
Editorial / European Journal of Operational Research 177 (2007) 1520–1522
which include many unresolved problems, such as multiobjective games, uncertain MOPGP, and dynamic MOPGP. Other papers attempt to generate the Pareto set for combinatorial MOPGPs by the use of exact methods and heuristics. Many real and interesting applications in network security, location, and resource allocation are also reported. 1.1. New trends Marmol, Monroy and Rubiales propose an equitable solution for multicriteria bargaining games. Their solution is based on minimizing a distance that involves a compromise among the levels reached for the different criteria. The solution is obtained by solving a finite sequence of min–max problems. Trzaskalik and Sitarz generalize Belman’s principle in order to solve multiobjective dynamic programming problems. Numerical examples show that the Pareto set seems to be very sensitive to the number of states and to problem size. Jabeur and Martel propose 3 procedures for building a collective choice method based on an aggregation of the individual-preference relations. The collective choice is obtained by minimizing a weighted distance to individual-preference structures under different considerations. The proposed method allows the identification of the subset of best alternatives, without ignoring any information from the graph of the preference relation structure. Engau and Wiecek revisit the problem of generating an epsilon-efficient solution posed by Loridan in 1984 and White in 1986. They propose a generic procedure to compute the epsilon-efficient set and describe some real problems where such a set is of interest. Yaghoobi and Tamiz apply the conventional min–max approach to solve fuzzy goal programs. They prove that their method is a generalization of the Hannan model (1986) and is equivalent to the formulation of Yang et al. (1991). A numerical example is provided to demonstrate the strengths of the new approach. Kaminski attempts to characterize preference relations that can be represented by multiobjective functions. He provides necessary and sufficient conditions for equivalence between a preference relation and a multiobjective function and presents
1521
two examples of preference models that cannot be represented by a multiobjective function. Jimenez, Arenas Bilbao and Rodriguez propose an interactive method to solve fuzzy linear programs. They use a fuzzy ranking method to evaluate the solutions and to interact with the DM. The method is illustrated on a numerical example. Hirschberger, Qi and Steuer present a procedure for the random generation of valid covariance matrices whose diagonal and off-diagonal elements possess a pre-specified expected values and standard deviations. The random covariance matrix generation capability provides a robust tool for generating test problems in the portfolio selection area of finance. 1.2. Generation of the Pareto set for combinatorial problems Nowak proposes an interactive method to solve a discrete, multiple-criteria decision making problem. The interactive method progressively reduces the set of feasible actions by combining the stochastic dominance technique with the preference threshold provided by the DM. Lemesre, Dhaenens and Talbi propose an exact method, based on the two phase method, to solve a bi-objective combinatorial problem. The authors provide a parallel version of their method to speed up the search for the Pareto set. Gomes da Silva, Figueira and Climaco address the bi-criteria knapsack problem and propose a hybrid approach mixing systematic and heuristic searches to identify interesting subsets of the feasible region to be examined in greater detail. They compare their results with results from exact methods and heuristics to show that their method performs well. Large, Jones and Tamiz are interested in the convergence of multiobjective evolutionary algorithms to the Pareto set. They propose a new method that transforms the decision space, using hyper-spherical inversions, to generate a solution set that converges to the Pareto set. Elaoud, Loukil and Teghem propose a Pareto fitness genetic algorithm for multiobjective optimization problems. Their method uses a fitness function based on a modified ranking procedure. Computational results are provided for six
1522
Editorial / European Journal of Operational Research 177 (2007) 1520–1522
multiobjective benchmarks to illustrate the accuracy of the proposed method. Calvete, Gale, Oliveros and Sanchez-Valverde investigate the use of goal programming to solve multiobjective vehicle routing problems with soft time windows. Their solution is based on an enumeration followed by an optimization approach. The enumeration step computes feasible routes, while the optimization step selects the best ones. Experimentation shows that the method is adequate for reasonably sized problems. 1.3. Applications Bozec and Dia utilize Data Envelopment Analysis to measure the board-performance of 14 Canadian state-owned enterprises. The analysis shows a positive relation between board size, board independence, and firm technical efficiency for deregulated companies. It appears from their analysis that when state owned enterprises are faced with market discipline, they are more effective at coping with their uncertain environments. Caballero, Conzalez, Guerrero, Molina and Paralera propose a multiobjective location-routing method to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. They apply their method to locate two incineration plants in the region of Andalusia (Spain) and to design the routes to serve the slaughterhouses in the region. Chu proposes a goal programming model for an integrated problem of assigning duties to the crew for the baggage services section at the Hong Kong International Airport. The results obtained minimize idle shifts, while satisfying various work conditions. Belfares, Klibi, Lo and Guitouni are interested in the military multiobjective resource-allocation problem. They investigate heuristic ways to generate the Pareto set. The solutions are generated by a tabu search technique and evaluated by combining a dominance rule and a multicriteria filtering method. Dhahri and Chabchoub propose a nonlinear goal programming model for the bullwhip effect. They incorporate in their model the DM preference by considering the concept of satisfaction
function. Two procedures are proposed. The first concerns a product demand generated with an autoregressive model with no lead-time; the second with a lead-time of two periods. The paper shows that combining forecasting methods with goal programming helps in managing demand variability. Ben Abdelaziz, Aouni and El-Fayedh propose a program to solve a portfolio selection problem by considering the DMs conflicting objectives and randomness of the returns. The proposed mathematical program combines the compromise-programming approach and the chance-constrained approach to handle both the stochastic and multiobjective aspects. The program is tested on the Tunisian Stock Market and compared to the solution provided when randomness is not considered. Fessi, Hamdi, Benabdallah and Boudrigua model the problem of network intrusion. They propose a multiattribute approach to help experts in finding the best response to a security incident. They provide a cost model that assesses the cost and benefit of a security response. The cost model allows them to build an appropriate multiattribute security algorithm. An illustrative example inspired by a security challenge is also presented. Kharrat, Chabchoub, Aouni and Smaoui propose an estimation model for cases with serial correlation through the imprecise GP model. The proposed model enables incorporating imprecise dependent variables with serial correlation and integrating explicitly the DM’s preferences for error terms. The authors present a numerical example to illustrate their method. Fouad Ben Abdelaziz Institut Supe´rieur de Gestion de Tunis, University of Tunis, Tunisia, Visiting at the Olayan School of Business, The American University of Beirut, PO Box 11-0236, Riad El Solh, Beirut, Lebanon Tel.: +9611374444; fax: +9611750214 E-mail addresses: [email protected], [email protected] Available online 15 February 2006
Editorial
Multiple objective programming and goal programming: New trends and applications
Multiple Objective Programming and Goal Programming (MOPGP) is a well-established area within the field of operational research. Being able to consider conflicting objectives enables the modeling many more problems in business, economics, and engineering. In the MOPGP paradigm, the decision aspects of the issues concerned are taken into account even during the solution steps, that is, the decision maker (DM) is at least as important as the modeler. Most multiobjective techniques and concepts have been developed over the past 30 years to deal with the huge variety of complex problems that can be solved by effecting trade-offs among conflicting interests. The types of problems addressed by MOPGP can be classified as to whether they are deterministic or non-deterministic, static or dynamic, continuous or discrete, linear or non-linear, etc. The generation of the Pareto set for convex problems has in general been well addressed. Sensitivity analysis and duality have been considered and studied with reference to multiobjective problems. Many interactive methods have been proposed and utilized to address real-life situations. For the combinatorial case, exact and heuristic methods have been developed to generate or approximate the Pareto set for many classical problems, such as the traveling salesman problem, the knapsack problem, and various scheduling problems. Meanwhile, a variety of goal programming techniques have been proposed and utilized. Goal pro-
gramming, along with its many variants, can now be considered as one of the most effective strategies for solving multiobjective optimization problems. Yet, for all the progress that has been achieved, many problems remain unresolved. To date, we are still unable to generate the entire Pareto set in many cases. Multiobjective stochastic optimization problems need more study. Formulations of multiobjective game problems are not complete. We do not know how to solve dynamic multiobjective problems. For all these cases, two main questions must be answered: what kind of solutions are we looking for and how to find these solutions? This Feature Cluster of EJOR contains a set of refereed papers selected from those presented at the 6th International Conference on Multiple Objective Programming and Goal Programming: New Trends and Applications (MOPGP’04. http://mopgp04.cjb.cc/), held in the village of Hammamet, Tunisia from 4th to 6th of April 2004. The Conference was attended by over 100 participants from 18 countries. In all, 46 papers were submitted for publication out of which 22 have been accepted for the Feature Cluster.
1. Content Some of the accepted papers focus on new trends in MOPGP. By new trends we mean aspects of MOPGP that have not been extensively addressed,
0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.12.023
Editorial / European Journal of Operational Research 177 (2007) 1520–1522
which include many unresolved problems, such as multiobjective games, uncertain MOPGP, and dynamic MOPGP. Other papers attempt to generate the Pareto set for combinatorial MOPGPs by the use of exact methods and heuristics. Many real and interesting applications in network security, location, and resource allocation are also reported. 1.1. New trends Marmol, Monroy and Rubiales propose an equitable solution for multicriteria bargaining games. Their solution is based on minimizing a distance that involves a compromise among the levels reached for the different criteria. The solution is obtained by solving a finite sequence of min–max problems. Trzaskalik and Sitarz generalize Belman’s principle in order to solve multiobjective dynamic programming problems. Numerical examples show that the Pareto set seems to be very sensitive to the number of states and to problem size. Jabeur and Martel propose 3 procedures for building a collective choice method based on an aggregation of the individual-preference relations. The collective choice is obtained by minimizing a weighted distance to individual-preference structures under different considerations. The proposed method allows the identification of the subset of best alternatives, without ignoring any information from the graph of the preference relation structure. Engau and Wiecek revisit the problem of generating an epsilon-efficient solution posed by Loridan in 1984 and White in 1986. They propose a generic procedure to compute the epsilon-efficient set and describe some real problems where such a set is of interest. Yaghoobi and Tamiz apply the conventional min–max approach to solve fuzzy goal programs. They prove that their method is a generalization of the Hannan model (1986) and is equivalent to the formulation of Yang et al. (1991). A numerical example is provided to demonstrate the strengths of the new approach. Kaminski attempts to characterize preference relations that can be represented by multiobjective functions. He provides necessary and sufficient conditions for equivalence between a preference relation and a multiobjective function and presents
1521
two examples of preference models that cannot be represented by a multiobjective function. Jimenez, Arenas Bilbao and Rodriguez propose an interactive method to solve fuzzy linear programs. They use a fuzzy ranking method to evaluate the solutions and to interact with the DM. The method is illustrated on a numerical example. Hirschberger, Qi and Steuer present a procedure for the random generation of valid covariance matrices whose diagonal and off-diagonal elements possess a pre-specified expected values and standard deviations. The random covariance matrix generation capability provides a robust tool for generating test problems in the portfolio selection area of finance. 1.2. Generation of the Pareto set for combinatorial problems Nowak proposes an interactive method to solve a discrete, multiple-criteria decision making problem. The interactive method progressively reduces the set of feasible actions by combining the stochastic dominance technique with the preference threshold provided by the DM. Lemesre, Dhaenens and Talbi propose an exact method, based on the two phase method, to solve a bi-objective combinatorial problem. The authors provide a parallel version of their method to speed up the search for the Pareto set. Gomes da Silva, Figueira and Climaco address the bi-criteria knapsack problem and propose a hybrid approach mixing systematic and heuristic searches to identify interesting subsets of the feasible region to be examined in greater detail. They compare their results with results from exact methods and heuristics to show that their method performs well. Large, Jones and Tamiz are interested in the convergence of multiobjective evolutionary algorithms to the Pareto set. They propose a new method that transforms the decision space, using hyper-spherical inversions, to generate a solution set that converges to the Pareto set. Elaoud, Loukil and Teghem propose a Pareto fitness genetic algorithm for multiobjective optimization problems. Their method uses a fitness function based on a modified ranking procedure. Computational results are provided for six
1522
Editorial / European Journal of Operational Research 177 (2007) 1520–1522
multiobjective benchmarks to illustrate the accuracy of the proposed method. Calvete, Gale, Oliveros and Sanchez-Valverde investigate the use of goal programming to solve multiobjective vehicle routing problems with soft time windows. Their solution is based on an enumeration followed by an optimization approach. The enumeration step computes feasible routes, while the optimization step selects the best ones. Experimentation shows that the method is adequate for reasonably sized problems. 1.3. Applications Bozec and Dia utilize Data Envelopment Analysis to measure the board-performance of 14 Canadian state-owned enterprises. The analysis shows a positive relation between board size, board independence, and firm technical efficiency for deregulated companies. It appears from their analysis that when state owned enterprises are faced with market discipline, they are more effective at coping with their uncertain environments. Caballero, Conzalez, Guerrero, Molina and Paralera propose a multiobjective location-routing method to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. They apply their method to locate two incineration plants in the region of Andalusia (Spain) and to design the routes to serve the slaughterhouses in the region. Chu proposes a goal programming model for an integrated problem of assigning duties to the crew for the baggage services section at the Hong Kong International Airport. The results obtained minimize idle shifts, while satisfying various work conditions. Belfares, Klibi, Lo and Guitouni are interested in the military multiobjective resource-allocation problem. They investigate heuristic ways to generate the Pareto set. The solutions are generated by a tabu search technique and evaluated by combining a dominance rule and a multicriteria filtering method. Dhahri and Chabchoub propose a nonlinear goal programming model for the bullwhip effect. They incorporate in their model the DM preference by considering the concept of satisfaction
function. Two procedures are proposed. The first concerns a product demand generated with an autoregressive model with no lead-time; the second with a lead-time of two periods. The paper shows that combining forecasting methods with goal programming helps in managing demand variability. Ben Abdelaziz, Aouni and El-Fayedh propose a program to solve a portfolio selection problem by considering the DMs conflicting objectives and randomness of the returns. The proposed mathematical program combines the compromise-programming approach and the chance-constrained approach to handle both the stochastic and multiobjective aspects. The program is tested on the Tunisian Stock Market and compared to the solution provided when randomness is not considered. Fessi, Hamdi, Benabdallah and Boudrigua model the problem of network intrusion. They propose a multiattribute approach to help experts in finding the best response to a security incident. They provide a cost model that assesses the cost and benefit of a security response. The cost model allows them to build an appropriate multiattribute security algorithm. An illustrative example inspired by a security challenge is also presented. Kharrat, Chabchoub, Aouni and Smaoui propose an estimation model for cases with serial correlation through the imprecise GP model. The proposed model enables incorporating imprecise dependent variables with serial correlation and integrating explicitly the DM’s preferences for error terms. The authors present a numerical example to illustrate their method. Fouad Ben Abdelaziz Institut Supe´rieur de Gestion de Tunis, University of Tunis, Tunisia, Visiting at the Olayan School of Business, The American University of Beirut, PO Box 11-0236, Riad El Solh, Beirut, Lebanon Tel.: +9611374444; fax: +9611750214 E-mail addresses: [email protected], [email protected] Available online 15 February 2006