This paper considers a capacitated vehicle routing problem with fuzzy random travel time and demand (FRVRP). A chance-constrained multiobjective programming is presented based on fuzzy random theory and converted to a crisp equivalent models under some assumptions. To solve such a multiobjective combinatorial optimization problem, this paper presents a hybrid multiobjective particle swarm optim...

In this paper the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality cond...

In this paper, Antczak’s -approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the -saddle points of the associated -approximated vector optimisation problems. We introduce an -Lagrange function for a constructed -approximated vector optimisation problem and present some modified -saddle point results. Furthermore, we construct an -ap...

  We suggest a method for finding the non-dominated points of the production possibility set (PPS) with variable returns to scale (VRS) technology in data envelopment analysis (DEA). We present a multiobjective linear programming (MOLP) problem whose feasible region is the same as the PPS under variable returns to scale for generating non-dominated points. We demonstrate that Pareto solutions o...

In this paper, a novel multiobjective evolutionary algorithm for optimal reactive power (VAR) dispatch problem is presented. The optimal VAR dispatch problem is formulated as a nonlinear constrained multiobjective optimization problem where the real power loss and the bus voltage deviations are to be minimized simultaneously. A new Strength Pareto Evolutionary Algorithm (SPEA) based approach is...

Robust design optimization (RDO) problems can generally be formulated by incorporating uncertainty into the corresponding deterministic problems. In this context, a careful formulation of deterministic equality constraints into the robust domain is necessary to avoid infeasible designs under uncertain conditions. The challenge of formulating equality constraints is compounded in multiobjective ...

In this paper we systematically study the importance, i.e., the influence on performance, of the main design elements that differentiate scalarizing functions-based multiobjective evolutionary algorithms (MOEAs). This class of MOEAs includes Multiobjecitve Genetic Local Search (MOGLS) and Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) and proved to be very successful in m...

This chapter will focus on the multiobjective formulation of an optimization problem and highlight the assets of a multiobjective Tabu implementation for such problems. An illustration of a specific Multiobjective Tabu heuristic (referred to as MO Tabu in the following) will be given for 2 particular problems arising in wireless systems. The first problem addresses the planning of access points...

The relationship between mathematical programming and classical calculus of variation was explored and extended by Hanson [6]. Thereafter variational programming problems have attracted some attention in literature. Duality for multiobjective variational problems has been of much interest in the recent years, and several contributions have been made to its development (see, e.g., Bector and Hus...

The 0/1 knapsack problem is a well-known problem, which appears in many real domains with practical importance. The problem is NP-complete. The multiobjective 0/1 knapsack problem is a generalization of the 0/1 knapsack problem in which multiple knapsacks are considered. Many algorithms have been proposed in the past five decades for both single and multiobjective knapsack problems. A new versi...