Survey of multi-objective optimization methods for engineering

A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

[1]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[2]  Abraham Charnes,et al.  Optimal Estimation of Executive Compensation by Linear Programming , 1955 .

[3]  K. B. Williams,et al.  Management Models and Industrial Applications of Linear Programming , 1962 .

[4]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[5]  Robert T. Eckenrode,et al.  Weighting Multiple Criteria , 1965 .

[6]  D. A. Conway.  Management Goals and Accounting for Control , 1966 .

[7]  A. Charnes,et al.  EFFECTIVE CONTROL THROUGH COHERENT DECENTRALIZATION WITH PREEMPTIVE GOALS , 1967 .

[8]  F. Waltz.  An engineering approach: Hierarchical optimization criteria , 1967, IEEE Transactions on Automatic Control.

[9]  N. Dopuch,et al.  Management Goals and Accounting for Control. , 1967 .

[10]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .

[11]  Morton D. Davis.  Game Theory: A Nontechnical Introduction , 1970 .

[12]  D. J. Cavicchio,et al.  Adaptive search using simulated evolution , 1970 .

[13]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[14]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

[15]  G. Leitmann,et al.  Compromise Solutions, Domination Structures, and Salukvadze’s Solution , 1974 .

[16]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[17]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[18]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[19]  Ambrose Goicoechea,et al.  Multiobjective programing in watershed management: A study of the Charleston Watershed , 1976 .

[20]  JiGuan G. Lin.  Multiple-objective problems: Pareto-optimal solutions by method of proper equality constraints , 1976 .

[21]  Richard E. Wendell,et al.  Efficiency in multiple objective optimization problems , 1977, Math. Program..

[22]  G. Leitmann.  Some problems of scalar and vector-valued optimization in linear viscoelasticity , 1977 .

[23]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[24]  W. Stadler.  Natural Structural Shapes of Shallow Arches , 1977 .

[25]  A. Osyczka.  An approach to multicriterion optimization problems for engineering design , 1978 .

[26]  H. P. Benson,et al.  Existence of efficient solutions for vector maximization problems , 1978 .

[27]  E. Gerasimov,et al.  Multicriterial optimization , 1978 .

[28]  W. Stadler.  NATURAL STRUCTURAL SHAPES (THE STATIC CASE) , 1978 .

[29]  Edward J. Haug,et al.  Applied optimal design: Mechanical and structural systems , 1979 .

[30]  John Casti,et al.  Vector-valued optimization problems in control theory , 1979 .

[31]  C. Hwang.  Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[32]  David G. Carmichael,et al.  Computation of pareto optima in structural design , 1980 .

[33]  H. W. Corley,et al.  A new scalar equivalence for Pareto optimization , 1980 .

[34]  Robert J. Krueger,et al.  A multiobjective optimization model for water resources planning , 1980 .

[35]  Singiresu S Rao,et al.  OPTIMUM DESIGN OF SHOCK AND VIBRATION ISOLATION SYSTEMS USING GAME THEORY , 1980 .

[36]  B. Hobbs.  A COMPARISON OF WEIGHTING METHODS IN POWER PLANT SITING , 1980 .

[37]  K. Kaza,et al.  Aeroelastic characteristics of a cascade of mistuned blades in subsonic and supersonic flows , 1983 .

[38]  Andrzej Osyczka,et al.  An Approach to Multicriterion Optimization for Structural Design , 1981 .

[39]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[40]  P. Vincke,et al.  Multicriteria analysis: survey and new directions , 1981 .

[41]  T. L. Vincent,et al.  Optimality in parametric systems , 1981 .

[42]  J. Koski.  Multicriterion Optimization in Structural Design , 1981 .

[43]  Kwangsun Yoon,et al.  Systems selection by multiple attribute decision making , 1982 .

[44]  A. Wierzbicki.  A Mathematical Basis for Satisficing Decision Making , 1982 .

[45]  J. Voogd,et al.  Multicriteria evaluation for urban and regional planning , 1982 .

[46]  Simon French,et al.  Multi-Objective Decision Analysis with Engineering and Business Applications , 1983 .

[47]  T. L. Vincent,et al.  Game Theory as a Design Tool , 1983 .

[48]  Ralph E. Steuer,et al.  An interactive weighted Tchebycheff procedure for multiple objective programming , 1983, Math. Program..

[49]  Eng Ung Choo,et al.  Proper Efficiency in Nonconvex Multicriteria Programming , 1983, Math. Oper. Res..

[50]  William K. Smith.  Multiobjective decision analysis with engineering and business applications , 1983 .

[51]  M. Bendsøe,et al.  A Variational Formulation for Multicriteria Structural Optimization , 1983 .

[52]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[53]  Andrzej Osyczka,et al.  Multicriterion optimization in engineering with FORTRAN programs , 1984 .

[54]  I. Kaliszenski.  A characterization of properly efficient solutions by an augmented Tchebycheff norm , 1985 .

[55]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[56]  J. Koski.  Defectiveness of weighting method in multicriterion optimization of structures , 1985 .

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

[58]  David E. Goldberg,et al.  ENGINEERING OPTIMIZATION VIA GENETIC ALGORITHM, IN WILL , 1986 .

[59]  W. Stadler,et al.  A survey of vector optimization in infinite-dimensional spaces, part 2 , 1986 .

[60]  A. Wierzbicki.  A methodological approach to comparing parametric characterizations of efficient solutions , 1986 .

[61]  K. Jörnsten,et al.  An entropy target-point approach to multiobjective programming , 1986 .

[62]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[63]  J. Koski,et al.  Norm methods and partial weighting in multicriterion optimization of structures , 1987 .

[64]  Singiresu S. Rao.  Game theory approach for multiobjective structural optimization , 1987 .

[65]  W. Stadler.  Initiators of Multicriteria Optimization , 1987 .

[66]  Johannes Jahn,et al.  Recent Advances and Historical Development of Vector Optimization , 1987 .

[67]  Ignacy Kaliszewski,et al.  A modified weighted tchebycheff metric for multiple objective programming , 1987, Comput. Oper. Res..

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

[69]  Wolfram Stadler,et al.  Fundamentals of Multicriteria Optimization , 1988 .

[70]  Theodor Freiheit,et al.  Modified game theory approach to multiobjective optimization , 1988 .

[71]  Singiresu S. Rao,et al.  Game theory approach for the integrated design of structures and controls , 1988 .

[72]  W. Stadler.  Multicriteria Optimization in Engineering and in the Sciences , 1988 .

[73]  Juhani Koski,et al.  Multicriteria Truss Optimization , 1988 .

[74]  Stanley Zionts,et al.  Multiple criteria mathematical programming: an updated overview and several approaches , 1988 .

[75]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[76]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[77]  J. R. Rao,et al.  Fuzzy set theoretic approach of assigning weights to objectives in multieriteria decision making , 1989 .

[78]  In Schoenauer,et al.  Parallel Problem Solving from Nature , 1990, Lecture Notes in Computer Science.

[79]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[80]  C. Tseng,et al.  MINIMAX MULTIOBJECTIVE OPTIMIZATION IN STRUCTURAL DESIGN , 1990 .

[81]  Frank Kursawe,et al.  A Variant of Evolution Strategies for Vector Optimization , 1990, PPSN.

[82]  W. Daniel Hillis,et al.  Co-evolving parasites improve simulated evolution as an optimization procedure , 1990 .

[83]  Andrzej Osyczka,et al.  Multicriteria Design Optimization: Procedures and Applications , 1990 .

[84]  J. E. Samouilidis,et al.  4.5. Multiobjective programming , 1990 .

[85]  Christos Douligeris,et al.  Fairness in network optimal flow control: optimality of product forms , 1991, IEEE Trans. Commun..

[86]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[87]  Li Xingsi,et al.  AN ENTROPY-BASED AGGREGATE METHOD FOR MINIMAX OPTIMIZATION , 1992 .

[88]  Manohar P. Kamat,et al.  Multicriteria Optimization In Engineering: A Tutorial And Survey , 1993 .

[89]  Philip D. Straffin,et al.  Game theory and strategy , 1993 .

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

[91]  Ching-Lai Hwang,et al.  A new approach for multiple objective decision making , 1993, Comput. Oper. Res..

[92]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

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

[94]  Ashok D. Belegundu,et al.  Multi-objective optimization of laminated ceramic composites using genetic algorithms , 1994 .

[95]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .

[96]  Wlodzimierz Ogryczak,et al.  A Goal Programming model of the reference point method , 1994, Ann. Oper. Res..

[97]  B. Brosowski,et al.  Simple tests for multi-criteria optimality , 1994 .

[98]  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.

[99]  Antonio Rufián-Lizana,et al.  A characterization of weakly efficient points , 1995, Math. Program..

[100]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[101]  Ching-Lai Hwang,et al.  Multiple attribute decision making : an introduction , 1995 .

[102]  Philip D. Hattis,et al.  High Speed Civil Transport (HSCT) plane design using physical programming , 1995 .

[103]  W. Stadler.  Caveats and Boons of Multicriteria Optimization , 1995 .

[104]  O. A. Elwakeil,et al.  Global optimization methods for engineering applications: A review , 1995 .

[105]  Achille Messac,et al.  Physical programming - Effective optimization for computational design , 1996 .

[106]  P. Papalambros,et al.  A NOTE ON WEIGHTED CRITERIA METHODS FOR COMPROMISE SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION , 1996 .

[107]  A. Osyczka,et al.  A modified distance method for multicriteria optimization, using genetic algorithms , 1996 .

[108]  Philip D. Hattis,et al.  Physical programming design optimization for High Speed Civil Transport , 1996 .

[109]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[110]  Robert S. Germain,et al.  Large Scale Systems , 1996 .

[111]  Jasbir S. Arora,et al.  TWO ALGORITHMS FOR GLOBAL OPTIMIZATION OF GENERAL NLP PROBLEMS , 1996 .

[112]  Kwei-Jay Lin,et al.  A theory of lexicographic multi-criteria optimization , 1996, Proceedings of ICECCS '96: 2nd IEEE International Conference on Engineering of Complex Computer Systems (held jointly with 6th CSESAW and 4th IEEE RTAW).

[113]  Hisao Ishibuchi,et al.  Multi-objective genetic local search algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[114]  Dan Li,et al.  Multiobjective optimization of structures with and without control , 1996 .

[115]  H. Ishibuchi,et al.  Multi-objective genetic algorithm and its applications to flowshop scheduling , 1996 .

[116]  Dan M. Frangopol.  Optimal Performance of Civil Infrastructure Systems , 1997 .

[117]  F. Y. Cheng,et al.  A Generalized Center Method for Multiobjective Optimization , 1997 .

[118]  F. Cheng,et al.  Multiobjective Optimization Design with Pareto Genetic Algorithm , 1997 .

[119]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[120]  Mehrdad Tamiz,et al.  Goal programming, compromise programming and reference point method formulations: linkages and utility interpretations , 1998, J. Oper. Res. Soc..

[121]  Bruce H. Wilson,et al.  Physical Programming for Computational Control , 1998 .

[122]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[123]  F. Cheng,et al.  Genetic Algorithm Development for Multiobjective Optimization of Structures , 1998 .

[124]  M. Chiampi,et al.  Multi-objective optimisation with stochastic algorithms and fuzzy definition of objective function , 1998 .

[125]  R. Balling,et al.  GENETIC ALGORITHMS WITH MULTIPLE OBJECTIVES , 1998 .

[126]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[127]  Wei Chen,et al.  Quality utility : a Compromise Programming approach to robust design , 1999 .

[128]  Sou-Sen Leu,et al.  GA-BASED MULTICRITERIA OPTIMAL MODEL FOR CONSTRUCTION SCHEDULING , 1999 .

[129]  S. Azarm,et al.  On improving multiobjective genetic algorithms for design optimization , 1999 .

[130]  Margaret M. Wiecek,et al.  Augmented Lagrangian and Tchebycheff Approaches in Multiple Objective Programming , 1999, J. Glob. Optim..

[131]  Jasbir S. Arora,et al.  Optimal Design of H-Frame Transmission Poles for Earthquake Loading , 1999 .

[132]  Glynn J. Sundararaj,et al.  Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers , 2000 .

[133]  Achille Messac,et al.  From Dubious Construction of Objective Functions to the Application of Physical Programming , 2000 .

[134]  John W. Hartmann,et al.  Optimal multi-objective low-thrust spacecraft trajectories , 2000 .

[135]  A. Messac,et al.  Aggregate Objective Functions and Pareto Frontiers: Required Relationships and Practical Implications , 2000 .

[136]  Wei Chen,et al.  Exploration of the effectiveness of physical programming in robust design , 2000 .

[137]  C. Poloni,et al.  Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics , 2000 .

[138]  A. Messac,et al.  Mathematical and Pragmatic Perspectives of Physical Programming , 2001 .

[139]  Y. Xie,et al.  Multicriterion Evolutionary Structural Optimization Using the Weighting and the Global Criterion Methods , 2001 .

[140]  Masoud Rais-Rohani,et al.  Manufacturability-Based Optimization of Aircraft Structures Using Physical Programming , 2001 .

[141]  A. Messac,et al.  Generating Well-Distributed Sets of Pareto Points for Engineering Design Using Physical Programming , 2002 .

[142]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

[143]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[144]  A. Maria,et al.  Optimization of large-scale rigidified inflatable structures for housing using physical programming , 2004 .

[145]  Yasuo Fujii,et al.  Multicriterion optimization using interval analysis , 1990, Computing.

[146]  Ben · Tali.  A SMOOTHING TECHNIQUE FOR NONDIFFERENTIABLE OPTIMIZATION PROBLEMS , .