Multi-objective NSBGA-II control of HIV therapy with monthly output measurement

Tackling the fuzzy multi-objective linear fractional problem using a parametric approach

Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization because more than one target has to be taken into account. For the problem, we face the concept of efficient solutions which is an infinite set especially when the objectives are in conflict. Since a classical method generally comes out with only one efficient solution, thus introducing new efficient approaches is helpful and beneficial for the decision makers to make their decisions according to more possibilities. In this paper, we aim to consider the MOLFPP with fuzzy coefficients (FMOLFPP) where the concept of α - cuts is utilized so as to transform the fuzzy numbers into closed intervals and rank the fuzzy numbers as well. Consequently, the fuzzy problem is changed into an interval valued multi-objective linear fractional programming problem (IV-MOLFPP). Subsequently, the IV-MOLFPP is further changed into linear programming problems (LPPs) using a parametric approach, weighted sum and max-min methods. It is demonstrated that the solution obtained is at least a weakly ɛ - efficient solution, where the value of ɛ helps a decision maker (DM) to make his decision appropriately i.e. DMs chose more likely the solutions with the lowest value of ɛ. Numerical examples are solved to illustrate the method and comparison are made to show the accuracy, and the reliability of the proposed solutions.

Study on multi-objective nonlinear programming problem with rough parameters

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.