A survey of recent developments in multiobjective optimization

Aghezzaf, B., & Hachimi, M. (2000). Generalized invexity and duality in multiobjective programming problems. Journal of Global Optimization, 18, 91–101. Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network flows: theory, algorithms, and applications. Jersey: New Prentice–Hall. Ansoff, H. I. (1968). Corporate strategy. Harmandsworth: Penguin. Bell, D. E., & Raiffa, H. (1988). Risky choice revisited. In D. E. Bell, H. Raiffa & A. Tversky (Eds.), Decision making: descriptive, normative and prescriptive interactions (pp. 99–112). Cambridge: Cambridge University Press. Bhaskar, K. (1979). A multiple objective approach to capital budgeting. Accounting and Business Research, 9, 25–46. Bitran, G. R. (1977). Linear multiple objective programs with zero-one variables. Mathematical Programming, 13, 121–139. Bitran, G. R. (1979). Theory and algorithms for linear multiple objective programs with zero-one variables. Mathematical Programming, 17, 362–390. Bitran, G. R. (1981). Duality for nonlinear multi-criteria optimization problems. Journal of Optimization Theory and Applications, 35, 367–401. Bouri, A., Martel, J. M., & Chabchoub, H. (2002). A multi-criterion approach for selecting attractive portfolio. Journal of Multi-Criteria Decision Analysis, 11, 269–277. Brumbaugh-Smith, J., & Shier, D. (1989). An empirical investigation of some bicriterion-shortest path algorithms. European Journal of Operational Research, 43, 216–224. Camerini, P.M., Galbiati, G., & Maffioli, F. (1984). The complexity of multi-constrained spanning tree problems. In Theory of algorithms (pp. 53–101). Colloquium Pecs 1984. Chalmet, L. G., Lemonidis, L., & Elzinga, D. J. (1986). An algorithm for the bi-criterion integer programming problem. European Journal of Operations Research, 25, 292–300. Chankong, V., & Haimes, Y. Y. (1983). Multiobjective decision making theory and methodology. New York: Elsevier Science. Cloquette, J. F., Gerard, M., & Hadhri, M. (1995). An empirical analysis of Belgian daily returns using GARCH models. Cahiers Economiques de Bruxelles, 418, 513–535. Corley, H. W. (1985). Efficient spanning trees. Journal of Optimization Theory and Applications, 45, 481–485. Craven, B. D. (1981). Duality for the generalized convex fractional programs. In S. Schiable & W. T. Ziemba (Eds.), Generalized Concavity in Optimization and Economics (pp. 473–489). New York: Academic. Das, L. N., & Nanda, S. (1997). Symmetric dual multiobjective programming. European Journal of Operational Research, 97, 167–171. Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerical Mathematics, 1, 262–271. Eben-Chaime, M. (1996). Parametric solution for linear bicriteria knapsack models. Management Science, 42, 1565–1575. Egudo, R. (1989). Efficiency and generalized convex duality for multiobjective programs. Journal of Mathematical Analysis and Applications, 138, 84–94. Ehrgott, M., & Gandibleux, X. (2000). A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum, 22, 425–460. Etzioni, O., Hanks, S., Jiang, T., Karp, R. M., Madari, O., & Waarts, O. (1996). Efficient information gathering on the Internet. In Proceedings of the 37th IEEE symposium on foundations of computer science (pp. 234–243). Gandibleux, X., & Freville, A. (2000). Tabu search based procedure for solving the 0–1 multiobjective knapsack problem: the two objective case. Journal of Heuristics, 6, 361–383. Garfinkel, R. S., & Nemhauser, G. L. (1972). Integer programming. New York: Wiley. Geoffrion, A. M. (1968). Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications, 22, 618–630. Hachimi, M., & Aghezzaf, B. (2004). Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions. Journal of Mathematical Analysis and Applications, 296, 382–392. Haimes, Y. Y., Lasdon, L. S., & Wismer, D. A. (1971). On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man and Cybernetics, 1, 296–297. Hamacher, H. W., & Ruhe, G. (1994). On spanning tree problems with multipleobjectives. Annals of Operations Research, 52, 209–230. Hanson, M. A. (1961). A duality theorem in nonlinear programming with nonlinear constraints. Australian Journal of Statistics, 3, 67–71. Hanson, M. A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80, 545–550. Henig, M. I. (1985). The shortest path problem with two objective functions. European Journal of Operational Research, 25, 281–291. Hillermeier, C. (2001). Nonlinear multiobjective optimization: a generalized homotopy approach. Boston: Birkhauser Verlag. Huarng, F., Pulat, P. S., & Shih, L. (1996). A computational comparison of some bicriterion shortest path algorithms. Journal of the Chinese Institution of Industrial Engineers, 13, 121–125. Hurson, C., & Zopounidis, C. (1995). On the use of multi-criteria decision aid methods to portfolio selection. Journal of Euro-Asian Management, 1, 69–94. Jacquillat, B. (1972). Les modèles d’évaluation et de sélection des valeurs mobilières: panorama des recherches américaines. Analyse Financière, 11, 68–88. Jahn, J. (2004). Vector optimization: theory, applications and extensions. Berlin: Springer. Jeyakumar, V. (1985). Strong and weak invexity in mathematical programming. Methods of Operations Research, 55, 109–125. Jeyakumar, V., & Mond, B. (1992). On generalized convex mathematical programming. Journal of the Australian Mathematical Society, Series B, 34, 43–53. Ibaraki, T. (1987). Enumerative approaches to combinatorial optimization, part ii. Annals of Operations Research, 11, 343–602. Khan, Z., & Hanson, M. A. (1997). On ratio invexity in mathematical programming. Journal of Mathematical Analysis and Applications, 205, 330–336. Khoury, N., Marte, J. M., & Veilleux, M. (1993). Methode multicritere de selection de portefeuilles indiciels interantionaux. Acualite Economique, 69, 171–190. Klamroth, K., & Wiecek, M. (2000a). Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics, 47, 57–76. Klamroth, K., & Wiecek, M. (2000b). Time-dependent capital budgeting with multiple criteria. In Y. Y. Haimes & R. E. Steuer (Eds.), Lecture notes in economics and mathematical systems: Vol. 487. Research and practice in multiple criteria decision making (pp. 421–432). Berlin: Springer. Klamroth, K., Tind, J., & Zust, S. (2004). Integer programming duality in multiple objective programming. Journal of Global Optimization, 29, 1–18. Klein, D., & Hannan, E. (1982). An algorithm for the multiple objective integer linear programming problem. European Journal of Operations Research, 93, 378–385. Kostreva, M. M., & Wiecek, M. M. (1993). Time dependency in multiple objective dynamic programming. Journal of Mathematical Analysis and Applications, 173, 289–307. Kruskal, J. B. (1956). On the shortest spanning tree of a graph and the traveling salesman problem. In Proceedings of American mathematical society 7 (pp. 48–50). Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. In J. Neyman (Ed.), Proceedings of the second Berkeley symposium on mathematical statistics and probability (pp. 481–492). Los Angeles: University of California Press. Lee, S. M., & Lerro, A. J. (1974). Capital budgeting for multiple objectives. Management Science, 36, 1106–1119. Liang, Z. A., Huang, H. X., & Pardalos, P. M. (2001). Optimality conditions and duality for a class of nonlinear fractional programming problems. Journal of Optimization Theory and Applications, 110, 611–619. Liang, Z. A., Huang, H. X., & Pardalos, P. M. (2003). Efficiency conditions and duality for a class of multiobjective fractional programming problems. Journal of Global Optimization, 27, 447–471. Luc, D. T. (1984). On duality theory in multiobjective programming. Journal of Optimization Theory and Applications, 43, 557–582. Luc, D. T., & Schaible, S. (1997). Efficiency and generalized concavity. Journal of Optimization Theory and Applications, 94, 147–153. Maeda, T. (1994). Constraint qualifications in multiobjective optimization problems: differentiable case. Journal of Optimization Theory and Applications, 80, 483–500. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91. Martello, S., & Toth, P. (1990). Knapsack problems: algorithms and computer implementations. New York: Wiley. Martello, S., Pisinger, D., & Toth, P. (1997). New trends in exact algorithms for the 0–1 knapsack problem. In J. Barceló (Ed.), Proceedings of EURO/IMFORMS-97 (pp. 151–160), Barcelona Marusciac, I. (1982). On Fritz John type optimality criterion in multiobjective optimization. L’Analyse Numérique et la Theorie de l’Approximation, 11, 109–114. Miettinen, K. M. (1999). Nonlinear multiobjective optimization. Boston: Kluwer Academic. Mond, B., & Weir, T. (1981). Generalized concavity and duality. In S. Schaible & W. T. Ziemba (Eds.), Generalized convexity in optimization and economics (pp. 263–280). New York: Academic. Nakayama, H. (1985). Duality theory in vector optimization: an overview, decision making with multiple objectives. In Y.Y. Haimes & V. Chankong (Eds.), Lecture Notes in Economics and Mathematical Systems (Vol. 337, pp. 109–125). Berlin: Springer. Papadimitriou, C. H., & Yannakakis, M. (2000). On the approximability of trade-offs and optimal access of web sources, In Proceedings of the 41st annual symposium on foundations of computer science (pp. 86–92). Pardalos, P. M., Siskos, Y., & Zopounidis, C. (Eds.). (1995). Advances in multicriteria analysis. Netherlands: Kluwer Academic. Pareto, V. (1964). Course d’economie politique. Genève: Libraire Drotz. The first edition in 1986. Preda, V. (1992). On efficiency and duality for multiobjective programs. Journal of Mathematical Analysis and Applications, 166, 365–377. Prim, R. C. (1957). Shortest connection networks and some generations. Bell System Technical Journal, 36, 1389–1401. Ramos, R. M., Aloso, S., Sicilia, J., & González, C. (1998). The problem of the optimal biobjective spanning tree. European Journal of Operational Research, 111, 617–628. Reddy, L. V., & Mukherjee, R. N. (1999). Some results on mathematical programming with generalized ratio invexity. Journal of Mathematical Analysis and Applications, 240, 299–310. Rosenblatt, M. J., & Sinuany-Stern, Z. (1989). Generating the discrete efficient frontier to the capital budgeting problem. Operations Research, 37, 38–394. Ruíz-Canales, P., & Rufián-Lizana, A. (1995). A characterization of weakly efficient points. Mathematical Programming, 68, 205–212. Sawaragi, Y., Nakayama, H., & Tanino, T. (1985). Theory of multiobjective optimization. Orlando: Academic. Schweigert, D. (1990). Linear extensions and vector-valued spanning trees. Methods of Operations Research, 60, 219–222. Serafini, P. (1986). Some considerations about computational complexity for multi objective combinatorial problems. In J. Jahn & W. Krabs (Eds.), Lecture notes in economics and mathematical systems: Vol. 294. Recent advances and historical development of vector optimization (pp. 222–231). Berlin: Springer. Singh, C., & Hanson, M. A. (1991). Multiobjective fractional programming duality theory. Naval Research Logistics, 38, 925–933. Singh, C., Bhatia, D., & Rueda, N. (1996). Duality in nonlinear multiobjective programming using augmented Lagrangian functions. Journal of Optimization Theory and Applications, 88, 659–670. Skriver, A. J. V., & Andersen, K. A. (2000). A label correcting approach for solving bicriterion shortest path problems. Computers and Operations Research, 27, 507–524. Sniedovich, M. (1988). A multi-objective routing problem revisited. Engineering Optimization, 13, 99–108. Spronk, J., & Hallerbach, W. G. (1997). Financial modelling: where to go? With an illustration for portfolio management. European Journal of Operational Research, 99, 113–127. Steuer, R. E. (1986). Multiple criteria optimization: theory, computation and application. New York: Wiley. Steuer, R. E., & Na, P. (2003). Multiple criteria decision making combined with finance: a categorized bibliography. European Journal of Operational Research, 150, 496–515. Tanina, T., & Sawaragi, Y. (1979). Duality theory in multiobjective programming. Journal of Optimization Theory and Applications, 27, 509–529. Thanassoulis, E. (1985). Selecting a suitable solution method for a multiobjective programming capital budgeting problem. Journal of Business Finance and Accounting, 12, 453–471. Ulungu, E. L., & Teghem, J. (1994). Application of the two phases method to solve the bi-objective knapsack problem. Technical report, Dept. of Mathematics & Operational Research, Faculté Polytechnique de Mons, Mons, Belgium, 1994. Ulungu, E. L., & Teghem, J. (1997). Solving multiobjective knapsack problems by a branch and bound procedure. In J. N. Climaco (Ed.), Multicriteria analysis (pp. 269–278). New-York: Springer. Vial, J. P. (1983). Strong and weak convexity set and functions. Mathematics of Operations Research, 8, 231–259. Villarreal, B., & Karwan, M. H. (1981). Multicriteria integer programming: a hybrid dynamic programming recursive approach. Mathematical Programming, 21, 204–223. Visée, M., Teghem, J., Pirlot, M., & Ulungu, E. L. (1996). Two-phases method and branch and bound procedures to solve the bi-objective knapsack problem. Technical report, Department of Mathematics & Operational Research, Faculté Polytechnique de Mons, Belgium, 1996. Wang, S. (1991). Second-order necessary and sufficient conditions in multiobjective programming. Numerical functional Analysis and Applications, 12, 237–252. Warburton, A. (1987). Approximation of a Pareto optima in multiple-objective shortest-path problems. Operations Research, 35, 70–79. Weingartner, H. M. (1963). Mathematical programming and the analysis of capital budgeting problems. New Jersey: Prentice–Hall. Weir, T. (1990). A note on invex functions and duality in generalized fractional programming. Research report, Department of Mathematics, The University of New South Wales, ACT 2600, Australia. Weir, T., & Mond, B. (1988). Symmetric and self duality in multiobjective programming. Asia-Pacific Journal of Operational Research, 5, 124–133. Zadeh, L. (1963). Optimality and non-scalar-valued performance criteria. IEEE Transactions on Automatic Control, 8, 59–60. Zhou, G., & Gen, M. (1999). Genetic algorithm approach on multi-criteria minimum spanning tree problem. European Journal of Operational Research, 114, 141–152. Zopounidis, C. (1999). Multicriteria decision aid in financial management. European Journal of Operational Research, 119, 404–415.