Under certain mild condition, the Pareto-optimal set (PS) of a continuous multiobjective optimization problem, with m objectives, is a piece-wise continuous (m 1)-dimensional manifold. This regularity property is important, yet has been unfortunately ignored in many evolutionary multiobjective optimization (EMO) studies. The first work that explicitly takes advantages of this regularity propert...

We present a natural fitness function f for the multiobjective shortest path problem, which is a fundamental multiobjective combinatorial optimization problem known to be NP-hard. Thereafter, we conduct a rigorous runtime analysis of a simple evolutionary algorithm (EA) optimizing f . Interestingly, this simple general algorithm is a fully polynomial-time randomized approximation scheme (FPRAS)...

This paper considers a transportation problem for moving empty or laden containers for a logistic company. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such a...

In this paper multiobjective optimization problem simultaneously optimized using hybrid PS-ACO algorithm has been attempted. The methodology used in this paper is based upon the information sharing and movement of swarms or particles in a search space, and further applying ACO on the result obtained by the PSO. Multiobjective optimization problems are present at physical design level at partiti...

Recognising the multiobjective nature of the decision process for rehabilitation of water supply distribution systems, this paper presents a comparative study of two multiobjective evolutionary methods, namely, multiobjective genetic algorithm (MOGA) and strength Pareto evolutionary algorithm (SPEA). The analyses were conducted on a simple hypothetical network for cost minimisation and minimum ...

This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the e...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...