( , ) ρ Φ − invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

This work investigates a method to search practically desirable solutions expanding the objective space with additional fitness functions associated to particular decision variables. The aim is to find solutions around preferred values of the chosen variables while searching for optimal solutions in the original objective space. Solutions to be practically desirable are constrained to be within...

Abstract: An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton m...

Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to same Pareto-Front. Prevalent evolutionary algorithms are not purely designed search for solution subsets, whereas, MMMOPs demonstrate degraded performance in objective space. This motivates design of better addressing MMMOPs. The present work identifies c...

  Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop...

Based on the dominated deformation mechanisms of superplastic materials, an assumption for micro-damage evolution is presented. Then, a set of uni®ed viscoplastic-damage constitutive equations is proposed to model material hardening due to the increase of dislocation density and grain growth, as well as material softening due to intergranular void nucleation and growth. The effects of the harde...

A multi-objective evolutionary algorithm (MOEA) approach is presented in this paper. The algorithm (DFBMOEA) aims to improve convergence of Paretobased MOEAs to the true Pareto optimal set/Pareto front and remove decision maker interaction from the process. A novel distance function is used as a fitness function for MOEA. A range equalisation function and a reference vector are utilised to elim...

This paper addresses the optimal placement of static var compensators (SVCs) in a power system network in such a manner that power loss, voltage deviation and installation cost is minimized. Voltage deviation is minimized by improving voltage profile. The aim of this study is to minimizing the power loss, voltage deviation and installation cost under critical contingency and increasing load con...