Abstract
Many important topics in multiobjective optimization and decision making have been studied in this book so far. In this chapter, we wish to discuss some new trends and challenges which the field is facing. For brevity, we here concentrate on three main issues: new problem areas in which multiobjective optimization can be of use, new procedures and algorithms to make efficient and useful applications of multiobjective optimization tools and, finally, new interesting and practically usable optimality concepts. Some research has already been started and some such topics are also mentioned here to encourage further research. Some other topics are just ideas and deserve further attention in the near future.
Reviewed by: Jörg Fliege, University of Southampton, UK; Joshua Knowles, University of Manchester, UK; Jürgen Branke, University of Karlsruhe, Germany
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aittokoski, T., Miettinen, K.: Cost effective simulation-based multiobjective optimization in performance of internal combustion engine. Engineering Optimization 40(7), 593–612 (2008)
Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht (1998)
Belton, V., Stewart, T.J.: Multiple Criteria Decision Analysis. Kluwer Academic Publishers, Dordrecht (2001)
Bingul, Z.: Adaptive genetic algorithms applied to dynamic multiobjective problems. Applied Soft Computing 7(3), 791–799 (2007), doi:10.1016/j.asoc.2006.03.001.
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, Heidelberg (1997)
Blackmond, L.K., Fischer, G.W.: Estimating utility functions in the presence of response error. Management Science 33, 965–980 (1987)
Bleuler, S., Brack, M., Zitzler, E.: Multiobjective genetic programming: Reducing bloat using SPEA2. In: Proceedings of the 2001 Congress on Evolutionary Computation, pp. 536–543. IEEE Computer Society Press, Piscataway (2001)
Branke, J., Kauβler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 499–507 (2001)
Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding knees in multi-objective optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 722–731. Springer, Heidelberg (2004a)
Branke, J., Schmeck, H., Deb, K., Reddy, M.: Parallelizing multi-objective evolutionary algorithms: Cone separation. In: Proceedings of the Congress on Evolutionary Computation (CEC-2004), pp. 1952–1957. IEEE Press, Piscataway (2004b)
Bui, L.T., Abbass, H.A., Essam, D.: Fitness inheritance for noisy evolutionary multi-objective optimization. In: Proceedings of the International Conference on Genetic and evolutionary computation (GECCO-2005), pp. 779–785. ACM Press, New York (2005)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)
Deb, K., Chaudhuri, S.: I-MODE: An interactive multi-objective optimization and decision-making using evolutionary methods. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 788–802. Springer, Heidelberg (2007)
Deb, K., Gupta, H.: Searching for robust Pareto-optimal solutions in multi-objective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 150–164. Springer, Heidelberg (2005)
Deb, K., Kumar, A.: Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2007), pp. 781–788. ACM Press, New York (2007a)
Deb, K., Kumar, A.: ’Light beam search’ based multi-objective optimization using evolutionary algorithms. In: Proceedings of the Congress on Evolutionary Computation (CEC-2007), pp. 2125–2132. IEEE Computer Society Press, Piscataway (2007b)
Deb, K., Srinivasan, A.: Innovization: Innovating design principles through optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp. 1629–1636. ACM Press, New York (2006)
Deb, K., Zope, P., Jain, S.: Distributed computing of Pareto-optimal solutions with evolutionary algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 534–549. Springer, Heidelberg (2003)
Deb, K., Sundar, J., Reddy, U., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research 2(6), 273–286 (2006)
Deb, K., Rao N., U.B., Karthik, S.: Dynamic multi-objective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 803–817. Springer, Heidelberg (2007a)
Deb, K., Padmanabhan, D., Gupta, S., Mall, A.K.: Reliability-based multi-objective optimization using evolutionary algorithms. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 66–80. Springer, Heidelberg (2007b)
Delattre, M., Hansen, P.: Bicriterion cluster analysis. IEEE Transaction Pattern Analysis and Machine Intelligence 2(4), 277–291 (1980)
Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic Publishers, Dordrecht (2002)
Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52, 333–359 (2003)
Denda, R., Banchs, A., Effelsberg, W.: The fairness challenge in computer networks. In: Crowcroft, J., Roberts, J., Smirnov, M.I. (eds.) Quality of Future Internet Services, pp. 208–220. Springer, Heidelberg (2000)
Engineous Software, Inc.: iSIGHT Reference Guide Version 7.1, pp. 220–233. Engineous Software, Inc. (2002)
Eremeev, A.V., Reeves, C.R.: On confidence intervals for the number of local optima. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 224–235. Springer, Heidelberg (2003)
Farina, M., Deb, K., Amato, P.: Dynamic multiobjective optimization problems: Test cases, approximations, and applications. IEEE Transactions on Evolutionary Computation 8(5), 425–442 (2000)
Fliege, J.: The effects of adding objectives to an optimisation problem on the solution set. Operations Research Letters 35(6), 782–790 (2007)
Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms–Part I: A unified formulation. IEEE Transactions on Systems, Man and Cybernetics 28(1), 26–37 (1998)
Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications 22(3), 618–630 (1968)
Goel, A., Meyerson, A.: Simultaneous optimization via approximate majorization for concave profits or convex costs. Algorithmica 44, 301–323 (2006)
Gupta, S., Rosenhead, J.: Robustness in sequential investment decisions. Management Science 15, 18–29 (1968)
Hakanen, J., Miettinen, K., Mäkelä, M., Manninen, J.: On interactive multiobjective optimization with NIMBUS in chemical process design. Journal of Multi-Criteria Decision Analysis 13(2–3), 125–134 (2005)
Handl, J., Knowles, J.: An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation 11(1), 56–76 (2007)
Handl, J., Kell, D.B., Knowles, J.: Multiobjective optimization in bioinformatics and computational biology. ACM/IEEE Transactions on Computational Biology and Bioinformatics 4(2), 279–292 (2007)
Hites, R., De Smet, Y., Risse, N., Salazar-Neumann, M., Vincke, P.: About the applicability of MCDA to some robustness problems. European Journal of Operational Research 174, 322–332 (2006)
Hughes, E.J.: Evolutionary multi-objective ranking with uncertainty and noise. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 329–343. Springer, Heidelberg (2001)
Jahn, J.: Vector Optimization – Theory, Applications, and Extensions. Springer, Heidelberg (2004)
Jahn, J.: Introduction to the Theory on Nonlinear Optimization. Springer, Heidelberg (2007)
Jaszkiewicz, A., Słowiński, R.: The ‘light beam search’ approach – an overview of methodology and applications. European Journal of Operational Research 113, 300–314 (1999)
Jensen, M.T.: Helper-objectives: Using multi-objective evolutionary algorithms for single-objective optimisation. Journal of Mathematical Modelling and Algorithms 3(4), 323–347 (2004)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments. IEEE Transactions on Evolutionary Computation 9(3), 303–317 (2005)
Jin, Y., Sendhoff, B.: Trade-off between performance and robustness: An evolutionary multiobjective approach. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 237–251. Springer, Heidelberg (2003)
Kaliszewski, I.: Quantitative Pareto Analysis by Cone Separation Technique. Kluwer Academic Publishers, Dodrecht (1994)
Klamroth, K., Miettinen, K.: Integrating approximation and interactive decision making in multicriteria optimization. Operations Research 56(1), 222–234 (2008)
Knowles, J., Corne, D., Deb, K. (eds.): Multiobjective Problem Solving from Nature. Springer, Heidelberg (2008)
Knowles, J.D., Watson, R.A., Corne, D.W.: Reducing local optima in single-objective problems by multi-objectivization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 269–283. Springer, Heidelberg (2001)
Korhonen, P.: A visual reference direction approach to solving discrete multiple criteria problems. European Journal of Operational Research 34, 152–159 (1988)
Kostreva, M., Ogryczak, W., Wierzbicki, A.: Equitable aggregations and multiple criteria analysis. European Journal of Operational Research 158(2), 362–377 (2004)
Kostreva, M.M., Ogryczak, W.: Linear optimization with multiple equitable criteria. RAIRO Operations Research 33, 275–297 (1999)
Kouvelis, P., Yu, G.: Robust Discrete Optimization and Its Applications. Kluwer Academic Publishers, Dodrecht (1997)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 263–282 (2002)
Luss, H.: On equitable resource allocation problems: A lexicographic minimax approach. Operations Research 47, 361–378 (1999)
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston (1999)
Miettinen, K., Mäkelä, M.M.: Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Computers & Operations Research 27(7–8), 709–723 (2000)
Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research 170, 909–922 (2006)
Miettinen, K., Mäkelä, M.M., Männikkö, T.: Optimal control of continuous casting by nondifferentiable multiobjective optimization. Computational Optimization and Applications 11(2), 177–194 (1998)
Miettinen, K., Lotov, A.V., Kamenev, G.K., Berezkin, V.E.: Integration of two multiobjective optimization methods for nonlinear problems. Optimization Methods and Software 18, 63–80 (2003)
Miettinen, K., Mäkelä, M.M., Maaranen, H.: Efficient hybrid methods for global continuous optimization based on simulated annealing. Computers & Operations Research 33(4), 1102–1116 (2006)
Neumann, F., Wegener, I.: Minimum spanning trees made easier via multi-objective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2005), pp. 763–769. ACM Press, New York (2005)
Ogryczak, W.: On the distribution approach to location problems. Computers & Industrial Engineering 37, 595–612 (1999)
Ogryczak, W.: Multiple criteria optimization and decisions under risk. Control and Cybernetics 31, 975–1003 (2002)
Ogryczak, W., Ruszczyński, A.: From stochastic dominance to mean-risk models: Semideviations as risk measures. European Journal of Operational Research 116, 33–50 (1999)
Ogryczak, W., Wierzbicki, A., Milewski, M.: A multi-criteria approach to fair and efficient bandwidth allocation. Omega 36, 451–463 (2008)
Olson, D.: Decision Aids for Selection Problems. Springer, New York (1996)
Palaniappan, S., Zein-Sabatto, S., Sekmen, A.: Dynamic multiobjective optimization of war resource allocation using adaptive genetic algorithms. In: Proceedings of the IEEE Southeast Conference, pp. 160–165. Clemson University, Clemson, SC (2001)
Parmee, I.C., Cevtković, D., Watson, A.W., Bonham, C.R.: Multiobjective satisfaction within an interactive evolutionary design enviornment. Evolutionary Computation Journal 8(2), 197–222 (2000)
Perny, P., Spanjaard, O., Storme, L.-X.: A decision-theoretic approach to robust optimization in multivalued graphs. Annals of Operations Research 147, 317–341 (2006)
Pióro, M., Medhi, D.: Routing, Flow and Capacity Design in Communication and Computer Networks. Morgan Kaufmann, San Francisco (2004)
Romeijn, H.E., Ahuja, R.K., Dempsey, J.F., Kumar, A.: A new linear programming approach to radiation therapy treatment planning problems. Operations Research 54, 201–216 (2006)
Roy, B.: A missing link in OR-DA: Robustness analysis. Foundations of Computing and Decision Sciences 23, 141–160 (1998)
San Miguel, F., Ryan, M., Scott, A.: Are preferences stable? The case of health care. Journal of Economic Behavior and Organization 48, 1–14 (2002)
Shimoyama, K., Oyama, A., Fujii, K.: A new efficient and useful robust optimization approach – design for multi-objective six sigma. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 1, pp. 950–957. IEEE Computer Society Press, Piscataway (2005)
Teich, J.: Pareto-front exploration with uncertain objectives. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 314–328. Springer, Heidelberg (2001)
Thiele, L., Miettinen, K., Korhonen, P.J., Molina, J.: A preference-based interactive evolutionary algorithm for multiobjective optimization. Working Papers W-412, Helsinki School of Economics, Helsinki (2007)
von Stackelberg, H.: Marktform und Gleichgewicht. Springer, Berlin (1934)
von Winterfeldt, D., Edwards, W.: Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge (1986)
Wierzbicki, A.: On completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum 8, 73–87 (1986)
Yu, P.: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiple objectives. Journal of Optimization Theory and Applications 14, 319–377 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Miettinen, K., Deb, K., Jahn, J., Ogryczak, W., Shimoyama, K., Vetschera, R. (2008). Future Challenges. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds) Multiobjective Optimization. Lecture Notes in Computer Science, vol 5252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88908-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-88908-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88907-6
Online ISBN: 978-3-540-88908-3
eBook Packages: Computer ScienceComputer Science (R0)