In this article, we use a monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems which include many classes of captivating problems, for example when the criterion functions are nonlinear fractional. After the algorithm is terminated, with any given tolerance, an approximation of the weakly efficient solution set is obtained containing the whole weakly efficient solution set of the problem. The algorithm is proved to be convergent and it is suitable to be implemented in parallel using convex programming tools. Some computational experiments are reported to show the accuracy and efficiency of the algorithm.
AvrielM., DiewertW.E., SchaibleS. and ZangI., Generalized Concavity, Plenum Press, New York, (1988).
2.
BenoistJ., Contractibility of the efficient set in strictly quasi-concave vector maximization, Journal of Optimization Theory and Applications110 (2001), 325–336.
3.
BensonH.P., An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem, Journal of Global Optimization13 (1998), 1–24.
4.
BensonH.P., On the global optimization of sums of linear fractional functions over a convex set, Journal of Optimization Theory and Applications121 (2004), 19–39.
5.
BensonH.P., A global optimization approach for generating efficient points for multiobjective concave fractional programs, Journal of Multi-Criteria Decision Analysis13 (2005), 15–28.
6.
DasI. and DennisJ.E., Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems, SIAM Journal on Optimization8 (1998), 631–657.
7.
EhrgottM., ShaoL. and SchobelA., An Approximation Algorithm for Convex Multi-objective Programming Problems, Journal of Global Optimization50 (2011), 397–416.
8.
GourionD. and LucD.T., Finding efficient solutions by free disposal outer approximation, SIAM Journal on Optimization20 (2010), 2939–2958.
9.
KaliszewskiI., MiroforidisJ. and PodkopaevD., Interactive multiple criteria decision making based on preference driven evolutionary multiobjective optimization with controllable accuracy, European Journal of Operational Research216(1) (2012), 188–199.
10.
KlamrothK., TindJ. and WiecekM.M., Unbiased approximation in multicriteria optimization, Mathematical Methods of Operations Research56 (2002), 413–457.
11.
KonnoH. and InoriM., Bond portfolio optimization by bilinear fractional programming, Journal of the Operations Research Society of Japan32 (1989), 143–158.
12.
NobakhtianS. and ShafieiN., A Benson type algorithm for nonconvex multiobjective programming problems, TOP25 (2017), 271–287.
13.
LucD.T., Generalized Convexity in Vector Optimization, in: Handbook of Generalized Convexity and Generalized Monotonicity, Springer-Verlag, New York, (2005), pp. 195–136.
14.
MangasarianO.L., Nonlinear Programming, McGraw-Hill, New York, (1969).
15.
RuzikaS. and WiecekM.M., Approximation methods in multiobjective programming, Journal of Optimization Theory and Applications126 (2005), 473–501.
16.
SinghP., Weakly fuzzy efficient conditions for multiobjective fractional programming problem, Journal of Intelligent and Fuzzy Systems26 (2014), 1383–1392.
TuyH., Normal sets, polyblocks and monotonic optimization, Vietnam Journal of Mathematics27 (1999), 277–300.
19.
TuyH., Monotonic Optimization: Problems and Solution Approaches, SIAM Journal on Optimization2 (2000), 464–494.
20.
TuyH., Al-KhayyalF. and ThachP.T., Monotonic Optimization: Branch and Cuts Methods, in: Essays and Surveys on Global Optimization, Springer-Verlag, New York, (2005), pp. 39–78.
21.
VeeramaniC. and SumathiM., A new method for solving fuzzy linear fractional programming problems, Journal of Intelligent and Fuzzy Systems31 (2016), 1831–1843.
22.
WiecekM.M., EhrgottM. and EngauA., Continuous multiobjective programming, in: Multiple criteria decision analysis: State of the art surveys, Oper Res Manag Sci Springer, New York, (2016), pp. 739–815.
