In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

The Genetic Immune Strategy for Multiple Objective Optimization (GISMOO) is a hybrid algorithm for solving multiobjective problems. The performance of this approach has been assessed using a classical combinatorial multiobjective optimization benchmark: the multiobjective 0/1 knapsack problem (MOKP) [1] and two-dimensional unconstrained multiobjective problems (ZDT) [2]. This paper shows that t...

This paper presents a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem. A new Strength Pareto Evolutionary Algorithm (SPEA) based approach is proposed to handle the problem as a true multiobjective problem with competing and non-commensurable objectives....

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...

The Protein Structure Prediction problem, which involves correctly predicting the geometrical conformation of a fully folded protein, is extremely difficult to solve and there currently is no “best” method of generating solutions. This paper focuses on an energy minimization technique and the use of a multiobjective genetic algorithm, the multiobjective fast messy genetic algorithm (fmGA) to ob...

In this paper, we propose a multiobjective Genetic Algorithm (mo-GA) for solving a multiobjective reliability optimization problem. In order to obtain high efficiency of searching non-dominated solutions, we combine the Improved Saving Pareto solutions Strategy (ISPS) and the adoptive Local Search (LS) with the multiobjective Genetic Algorithm. Through some numerical experiments, we evaluate th...

The multiobjective bilevel program is a sequence of two optimization problems, with the upper-level problem being multiobjective and the constraint region of the upper level problem being determined implicitly by the solution set to the lower-level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of all lower-level problems near...