Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications

This chapter provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe their main characteristics, and review the main properties and theoretical results. One section is devoted to a brief description of the available solution methodology, both exact and heuristic. The main part of the chapter consists of an annotation of the existing literature in the field organized problem by problem. We conclude the chapter by stating open questions and areas of future research. The list of references comprises more than 400 entries.

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[58]  James P. Ignizio,et al.  A Multicriteria Approach to Supersystem Architecture Definition , 1982, IEEE Transactions on Computers.

[59]  Knut Richter,et al.  Solving a multiobjective traveling salesman problem by dynamic programming , 1982 .

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[63]  Samuel J. Ratick,et al.  A mixed integer and multiple objective programming model to analyze coal handling in New England , 1983 .

[64]  S. Ratick Multiobjective programming with related bargaining games An application to utility coal conversions , 1983 .

[65]  P. Harker,et al.  MULTICRITERIA SPATIAL PRICE EQUILIBRIUM NETWORK DESIGN: THEORY AND COMPUTATIONAL RESULTS , 1983 .

[66]  Richard M. Soland,et al.  The design of multiactivity multifacility systems , 1983 .

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[68]  Marc J. Schniederjans,et al.  A Multicriteria Assignment Problem: A Goal Programming Approach , 1983 .

[69]  Philippe Vincke Problèmes de localisation multicritères , 1983 .

[70]  W. Habenicht,et al.  Quad Trees, a Datastructure for Discrete Vector Optimization Problems , 1983 .

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[74]  D. J. White,et al.  A Special Multi-Objective Assignment Problem , 1984 .

[75]  F. Szidarovszky,et al.  Multiobjective management of mining under water hazard by game theory , 1984 .

[76]  Charles Sutcliffe,et al.  Goal Programming and Allocating Children to Secondary Schools in Reading , 1984 .

[77]  Sheila M. Lawrence,et al.  A Multiple objective shift allocation model , 1984 .

[78]  D. Klingman,et al.  Topological and Computational Aspects of Preemptive Multicriteria Military Personnel Assignment Problems , 1984 .

[79]  Daniel Granot A new exchange property for matroids and its application to max-min-problems , 1984, Z. Oper. Research.

[80]  Charles ReVelle,et al.  SYMPOSIUM ON LOCATION PROBLEMS: IN MEMORY OF LEON COOPER.: THE SHORTEST COVERING PATH PROBLEM: AN APPLICATION OF LOCATIONAL CONSTRAINTS TO NETWORK DESIGN , 1984 .

[81]  E. Martins On a multicriteria shortest path problem , 1984 .

[82]  E. Martins On a special class of bicriterion path problems , 1984 .

[83]  L Berghmans,et al.  Implementation of Health Facilities in a New City , 1984, The Journal of the Operational Research Society.

[84]  James P. Ignizio,et al.  A methodology for multicriteria network partitioning , 1984, Comput. Oper. Res..

[85]  Ernesto de Queirós Vieira Martins An algorithm to determine a path with minimal cost/capacity ratio , 1984, Discret. Appl. Math..

[86]  J. Current,et al.  The maximum covering/shortest path problem: A multiobjective network design and routing formulation , 1985 .

[87]  James F. Cox,et al.  Multiple criteria approach to the facilities layout problem , 1985 .

[88]  R. Deckro,et al.  Preference Trade-Offs In Capital Budgeting Decisions , 1985 .

[89]  R. Rosenthal,et al.  A Multiobjective Discrete Optimization Model for Land Allocation , 1985 .

[90]  J. D. Schaffer,et al.  Multiple Objective Optimization with Vector Evaluated Genetic Algorithms , 1985, ICGA.

[91]  Arthur Warburton,et al.  Worst case analysis of greedy and related heuristics for some min-max combinatorial optimization problems , 1985, Math. Program..

[92]  Roger Hartley Vector Optimal Routing by Dynamic Programming , 1985 .

[93]  N. K. Kwak,et al.  Goal programming solutions to transportation problems with variable supply and demand requirements , 1985 .

[94]  Hirotaka Nakayama,et al.  Theory of Multiobjective Optimization , 1985 .

[95]  H. W. Corley,et al.  Shortest paths in networks with vector weights , 1985 .

[96]  H. W. Corley,et al.  Efficient spanning trees , 1985 .

[97]  Leslie G. Valiant,et al.  NP is as easy as detecting unique solutions , 1985, STOC '85.

[98]  P. L. Kunsch,et al.  Interactive Methods for Multi-Objective Integer Linear Programming , 1986 .

[99]  L. M. Rasmussen Zero--one programming with multiple criteria , 1986 .

[100]  N. Sancho A MULTI-OBJECTIVE ROUTING PROBLEM , 1986 .

[101]  Pierre Hansen,et al.  Efficient points on a network , 1986, Networks.

[102]  Hemant Jain,et al.  Concepts, Theory, and Techniques DISTRIBUTED COMPUTER SYSTEM DESIGN: A MULTICRITERIA DECISION‐MAKING METHODOLOGY* , 1986 .

[103]  M. I. Henig The shortest path problem with two objective functions , 1986 .

[104]  Hokey Min,et al.  Multiobjective design of transportation networks: taxonomy and annotation , 1986 .

[105]  Yang Byung Park,et al.  A solution of vehicle routing problems in a multiple objective environment , 1986 .

[106]  Sang M. Lee,et al.  The Multi‐Criteria Warehouse Location Problem Revisited , 1987 .

[107]  I. Sergienko,et al.  Finding the set of alternatives in discrete multicriterion problems , 1987 .

[108]  Nancy V. Phillips,et al.  A Weighting Function for Pre-emptive Multicriteria Assignment Problems , 1987 .

[109]  B. Malakooti,et al.  Multiple objective programming for the quadratic assignment problem , 1987 .

[110]  Jared L. Cohon,et al.  THE MEDIAN SHORTEST PATH PROBLEM : A MULTIOBJECTIVE APPROACH TO ANALYZE COST VS. ACCESSIBILITY IN THE DESIGN OF TRANSPORTATION NETWORKS , 1987 .

[111]  E. Martins On a particular quadratic network problem , 1987 .

[112]  A. Warburton,et al.  Approximation Methods for Multiple Criteria Travelling Salesman Problems , 1987 .

[113]  J. Ringuest,et al.  Interactive solutions for the linear multiobjective transportation problem , 1987 .

[114]  Arthur Warburton,et al.  Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems , 1987, Oper. Res..

[115]  E. R. Clayton,et al.  A LINEAR GOAL PROGRAMMING MODEL OF A MULTI-PERIOD, MULTI-COMMODITY NETWORK FLOW PROBLEM , 1987 .

[116]  F. Robert Jacobs,et al.  A layout planning systems with multiple criteria and a variable domain representation , 1987 .

[117]  Timothy L. Urban A multiple criteria model for the facilities layout problem , 1987 .

[118]  Jeff R. Wright,et al.  MICROCOMPUTER-BASED MULTIOBJECTIVE PERSONNEL MANAGEMENT MODEL , 1987 .

[119]  Paolo Serafini,et al.  Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems , 1987 .

[120]  M. Goodchild,et al.  The Multiobjective Vending Problem: A Generalization of the Travelling Salesman Problem , 1988 .

[121]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[122]  Günther Ruhe,et al.  Complexity results for multicriterial and parametric network flows using a pathological graph of Zadeh , 1988, ZOR Methods Model. Oper. Res..

[123]  N. Sancho A new type of multi-objective routing problem , 1988 .

[124]  Krishan Rana,et al.  A Model and Solution Algorithm for Optimal Routing of a Time-Chartered Containership , 1988, Transp. Sci..

[125]  Ravindra K. Ahuja,et al.  Minimum cost-reliability ratio path problem , 1988, Comput. Oper. Res..

[126]  J. Current,et al.  The Minimum‐Covering/Shortest‐Path Problem* , 1988 .

[127]  Moshe Sniedovich,et al.  A MULTI-OBJECTIVE ROUTING PROBLEM REVISITED , 1988 .

[128]  Meir J. Rosenblatt,et al.  Generating the Discrete Efficient Frontier to the Capital Budgeting Problem , 1989, Oper. Res..

[129]  G. Rote,et al.  Approximation of convex curves with application to the bicriterial minimum cost flow problem , 1989 .

[130]  Włodzimierz Ogryczak,et al.  A solver for the multi-objective transshipment problem with facility location , 1989 .

[131]  Vicki Aaronson Hutson,et al.  Maximal Direct Covering Tree Problems , 1989, Transp. Sci..

[132]  B. Malakooti Multiple objective facility layout: a heuristic to generate efficient alternatives , 1989 .

[133]  Michel Minoux,et al.  Solving combinatorial problems with combined Min-Max-Min-Sum objective and applications , 1989, Math. Program..

[134]  Yang-Byung Park,et al.  An interactive computerized algorithm for multicriteria vehicle routing problems , 1989 .

[135]  C. Keller Algorithms to solve the orienteering problem: A comparison , 1989 .

[136]  D. Shier,et al.  An empirical investigation of some bicriterion shortest path algorithms , 1989 .

[137]  Jun Wang,et al.  A sensor-based accelerated approach for multi-attribute machinability and tool life evaluation , 1990 .

[138]  Charles Sutcliffe,et al.  Optimal Solution of a Vehicle-routeing Problem: Transporting Mentally Handicapped Adults to an Adult Training Centre , 1990 .

[139]  D. J. White,et al.  A Bibliography on the Applications of Mathematical Programming Multiple-objective Methods , 1990 .

[140]  Jared L. Cohon,et al.  An interactive approach to identify the best compromise solution for two objective shortest path problems , 1990, Comput. Oper. Res..

[141]  H. Moskowitz,et al.  Generalized dynamic programming for multicriteria optimization , 1990 .

[142]  Gunar E. Liepins,et al.  Genetic Algorithms Applications to Set Covering and Traveling Salesman Problems , 1990 .

[143]  Hokey Min,et al.  Multiobjective analysis of facility location decisions , 1990 .

[144]  Chelsea C. White,et al.  Multiobjective A* , 1991, JACM.

[145]  I. Murthy,et al.  A parametric approach to solving bicriterion shortest path problems , 1991 .

[146]  V. A. ev,et al.  Complexity of vector optimization problems on graphs , 1991 .

[147]  P. Simin Pulat,et al.  Bicriteria network flow problems: Continuous case , 1991 .

[148]  Dominique Peeters,et al.  Location on networks , 1992 .

[149]  H. Safer Fast approximation schemes for multi-criteria combinatorial optimization , 1992 .

[150]  Katta G. Murty,et al.  Network programming , 1992 .

[151]  P. Simin Pulat,et al.  Efficient solutions for the bicriteria network flow problem , 1992, Comput. Oper. Res..

[152]  Ernest H. Forman,et al.  Decision Support for Media Selection Using the Analytic Hierarchy Process , 1992 .

[153]  Ishwar Murthy,et al.  Solving min‐max shortest‐path problems on a network , 1992 .

[154]  Panagiotis Kouvelis,et al.  Total unimodularity applications in bi-objective discrete optimization , 1992, Oper. Res. Lett..

[155]  V. Emelichev,et al.  On cardinality of the set of alternatives in discrete many-criterion problems , 1992 .

[156]  Chelsea C. White,et al.  Multiobjective, preference-based search in acyclic OR-graphs , 1992 .

[157]  C. T. Tung,et al.  A multicriteria Pareto-optimal path algorithm , 1992 .

[158]  J. A. Hoogeveen,et al.  Single-machine bicriteria scheduling , 1992 .

[159]  Francesco Maffioli,et al.  Note on Combinatorial Optimization with Max-Linear Objective Functions , 1993, Discret. Appl. Math..

[160]  Vicki Aaronson Hutson,et al.  Indirect covering tree problems on spanning tree networks , 1993 .

[161]  M. Kostreva,et al.  Time Dependency in Multiple Objective Dynamic Programming , 1993 .

[162]  J. Shang Multicriteria facility layout problem: An integrated approach , 1993 .

[163]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[164]  T. Friesz,et al.  The multiobjective equilibrium network design problem revisited: A simulated annealing approach , 1993 .

[165]  Pitu B. Mirchandani,et al.  Multiobjective routing of hazardous materials in stochastic networks , 1993 .

[166]  Perry A. Appino,et al.  Approximating the noninferior set in multiobjective linear programming problems , 1993 .

[167]  Ralph E. Steuer,et al.  A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure , 1993 .

[168]  R. Bulfin,et al.  Complexity of single machine, multi-criteria scheduling problems , 1993 .

[169]  John R. Current,et al.  Multiobjective transportation network design and routing problems: Taxonomy and annotation , 1993 .

[170]  C. Reeves Modern heuristic techniques for combinatorial problems , 1993 .

[171]  Rakesh V. Vohra,et al.  Pareto optimality and a class of set covering heuristics , 1993, Ann. Oper. Res..

[172]  P. S. Pulat,et al.  Bicriteria network flow problems: Integer case , 1993 .

[173]  Maria João Alves,et al.  Interactive decision support for multiobjective transportation problems , 1993 .

[174]  Yash P. Aneja,et al.  A Generalized Time–Cost Trade-Off Transportation Problem , 1993 .

[175]  Horst W. Hamacher,et al.  On spanning tree problems with multiple objectives , 1994, Ann. Oper. Res..

[176]  I. Sigal Algorithms for solving the two-criterion large-scale travelling salesman problem , 1994 .

[177]  Paolo Serafini,et al.  Simulated Annealing for Multi Objective Optimization Problems , 1994 .

[178]  R. J. Gallagher,et al.  Constructing the set of efficient objective values in linear multiple objective transportation problems , 1994 .

[179]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[180]  M. I. Henig Efficient interactive methods for a class of multiattribute shortest path problems , 1994 .

[181]  B. Jaumard,et al.  A multi-criteria tabu search approach to cell formation problems in group technology with multiple objectives , 1994 .

[182]  Murat Köksalan,et al.  Scheduling with Multiple Criteria , 1994 .

[183]  Abraham P. Punnen,et al.  On combined minmax-minsum optimization , 1994, Comput. Oper. Res..

[184]  Zilla Sinuany-Stern,et al.  The One Dimensional Cutting Stock Problem Using Two Objectives , 1994 .

[185]  Reda M.S. Abd El-Aal An interactive technique for the cutting stock problem with multiple objectives , 1994 .

[186]  E. L. Ulungu,et al.  Multi‐objective combinatorial optimization problems: A survey , 1994 .

[187]  I. Murthy,et al.  An interactive procedure using domination cones for bicriterion shortest path problems , 1994 .

[188]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[189]  Herminia I. Calvete,et al.  An approach for the network flow problem with multiple objectives , 1995, Comput. Oper. Res..

[190]  Mario Calderini,et al.  A hierarchical bicriterion approach to integrated process plan selection and job shop scheduling , 1995 .

[191]  W. Ogryczak,et al.  The Multiple Criteria Location Problem: 1. A Generalized Network Model and the Set of Efficient Solutions , 1995 .

[192]  I. Melamed,et al.  An investigation of linear convolution of criteria in multicriteria discrete programming , 1995 .

[193]  Matthias Ehrgott Lexicographic Max-Ordering - A Solution Concept for Multicriteria Combinatorial Optimization , 1995 .

[194]  H. Ishibuchi,et al.  MOGA: multi-objective genetic algorithms , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[195]  Dominique Peeters,et al.  Chapter 7 Location on networks , 1995 .

[196]  Volker Nissen,et al.  On Using Penalty Functions and Multicriteria Optimisation Techniques in Facility Layout , 1995 .

[197]  J. A. Mesa,et al.  Multiobjective routing problems , 1995 .

[198]  Abraham P. Punnen,et al.  Minmax combinatorial optimization , 1995 .

[199]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[200]  D. Schweigert Vector-Weighted Matchings , 1995 .

[201]  Yong Shi A Transportation model with multiple criteria and multiple constraint levels , 1995 .

[202]  Horst W. Hamacher,et al.  A note onK best network flows , 1995, Ann. Oper. Res..

[203]  J. Orlin,et al.  Fast Approximation Schemes for Multi-Criteria Flow, Knapsack, and Scheduling Problems , 1995 .

[204]  Mauro Dell'Amico,et al.  on Some Multicriteria Arborescence Problems: Complexity and Algorithms , 1996, Discret. Appl. Math..

[205]  Minghe Sun,et al.  Quad-Trees and Linear Lists for Identifying Nondominated Criterion Vectors , 1996, INFORMS J. Comput..

[206]  Herminia I. Calvete,et al.  A Sequential Network-Based Approach for the Multiobjective Network Flow Problem with Preemptive Priorities , 1996 .

[207]  D. Lane,et al.  Interactive Multiple Criteria Optimization for Capital Budgeting in a Canadian Telecommunications Company , 1996 .

[208]  Mikael Lind,et al.  On bicriterion minimal spanning trees: An approximation , 1996, Comput. Oper. Res..

[209]  Masood A. Badri,et al.  A two-stage multiobjective scheduling model for [faculty-course-time] assignments , 1996 .

[210]  G. Tzeng,et al.  Fuzzy bicriteria multi-index transportation problems for coal allocation planning of Taipower , 1996 .

[211]  Mike Wright,et al.  A comparison of neighborhood search techniques for multi-objective combinatorial problems , 1996, Comput. Oper. Res..

[212]  M. Eben-Chaime Parametric solution for linear bicriteria knapsack models , 1996 .

[213]  Gilbert Laporte,et al.  Metaheuristics: A bibliography , 1996, Ann. Oper. Res..

[214]  Chan-Nan Lu,et al.  Implementation of network sensitivity calculation on vector computers , 1996 .

[215]  Minghe Sun,et al.  Solving Multiple Objective Programming Problems Using Feed-Forward Artificial Neural Networks: The Interactive FFANN Procedure , 1996 .

[216]  Abraham P. Punnen,et al.  An O(m log n) algorithm for the max + sum spanning tree problem , 1996 .

[217]  José Rui Figueira L'approche interactive dans le cas des problèmes de flot multicritères , 1996 .

[218]  Murat Köksalan,et al.  Note: Bicriteria scheduling for minimizing flow time and maximum tardiness , 1996 .

[219]  E. Ehrgott On matroids with multiple objectives , 1996 .

[220]  Lorraine R. Gardiner,et al.  A Bibliographic Survey of the Activities and International Nature of Multiple Criteria Decision Making , 1996 .

[221]  W. Ogryczak,et al.  The Multiple Criteria Location Problem: 2. Preference-Based Techniques and Interactive Decision Support , 1996 .

[222]  Alan D. Christiansen,et al.  An empirical study of evolutionary techniques for multiobjective optimization in engineering design , 1996 .

[223]  I. Melamed,et al.  A computational investigation of linear parametricization of criteria in multicriteria discrete programming , 1996 .

[224]  Kathrin Klamroth,et al.  Non-connected Efficiency Graphs in Multiple Criteria Combinatorial Optimization , 1997 .

[225]  Soung Hie Kim,et al.  An improved interactive hybrid method for the linear multi-objective knapsack problem , 1997, Comput. Oper. Res..

[226]  Pratyush Sen,et al.  A Multiple Criteria Genetic Algorithm for Containership Loading , 1997, ICGA.

[227]  C. Goh,et al.  A method for convex curve approximation , 1997 .

[228]  J. Teghem,et al.  Solving Multi-Objective Knapsack Problem by a Branch-and-Bound Procedure , 1997 .

[229]  M. Ehrgott,et al.  Equivalence of Balance Points and Pareto Solutions in Multiple-Objective Programming , 1997 .

[230]  Murat Köksalan,et al.  Bicriteria Scheduling: Minimizing Flowtime and Maximum Earliness on a Single Machine , 1997 .

[231]  João C. N. Clímaco,et al.  Multicriteria Integer Programming: An Overview of the Different Algorithmic Approaches , 1997 .

[232]  A. Jaszkiewicz,et al.  Fuzzy project scheduling with multiple criteria , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[233]  Andrzej Jaszkiewicz,et al.  Pareto Simulated Annealing , 1997 .

[234]  Wlodzimierz Ogryczak,et al.  On the lexicographic minimax approach to location problems , 1997, Eur. J. Oper. Res..

[235]  Adli Mustafa,et al.  Characteristics of the Efficient Solutions of Bicriteria and Tricriteria Network Flow Problems , 1997 .

[236]  M. John Hodgson,et al.  Testing a Bicriterion Location-Allocation Model with Real-World Network Traffic: The Case of Edmonton, Canada , 1997 .

[237]  Ernesto de Queirós Vieira Martins,et al.  An algorithm for the quickest path problem , 1997, Oper. Res. Lett..

[238]  Mauro Dell'Amico,et al.  Annotated Bibliographies in Combinatorial Optimization , 1997 .

[239]  Ralph E. Steuer,et al.  A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming , 1997, Oper. Res..

[240]  Minghe Sun Applying Tabu search to multiple objective combinatorial optimization problems , 1997 .

[241]  Xavier Gandibleux,et al.  A Tabu Search Procedure to Solve MultiObjective Combinatorial Optimization Problems , 1997 .

[242]  M. Ehrgott,et al.  Connectedness of efficient solutions in multiple criteria combinatorial optimization , 1997 .

[243]  I. Melamed,et al.  The linear convolution of criteria in the bicriteria traveling salesman problem , 1997 .

[244]  Minghe Sun,et al.  Tabu search multi-criteria decision model for facility location planning , 1997 .

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