NUMERICAL METHOD FOR THE SYSTEM OF REACTION-DIFFUSION EQUATIONS WITH A SMALL PARAMETER

This paper deals with the numerical method for the system of reaction-diffusion equations with a small parameter. It is difficult to solve the problems of this kind numerically because of the boundary layer efect Besed on singular perturbed theory and Greens function, we have established the difference scheme that is suited for the solution to the problems. We introduce an idea of feasitbe equidistant degree a here. And this proves that if a>2 the scheme converges in norm with speed uniformly.

A relative feasibility degree based approach for constrained optimization problems

Based on the ratio of the size of the feasible region of constraints to the size of the feasible region of a constrained optimization problem,we propose a new constraint handling approach to improve the efficiency of heuristic search methods in solving the constrained optimization problems.In the traditional classification of a solution candidate,it is either a feasible or an infeasible solution.To refine this classification,a new concept about the relative feasibility degree of a solution candidate is proposed to represent the amount by which the 'feasibility' of the solution candidate exceeds that of another candidate.Relative feasibility degree based selection rules are also proposed to enable evolutionary computation techniques to accelerate the search process of reaching a feasible region.In addition,a relative feasibility degree based differential evolution algorithm is derived to solve constraint optimization problems.The proposed approach is tested with nine benchmark problems.Results indicate that our approach is very competitive compared with four existing state-of-the-art techniques,though still sensitive to the intervals of control parameters of the differential evolution.

Research on the Optimization Approach for Cargo Oil Tank Design Based on the Improved Particle Swarm Optimization Algorithm

Based on the improved particle swarm optimization(PSO) algorithm,an optimization approach for the cargo oil tank design(COTD) is presented in this paper.The purpose is to design an optimal overall dimension of the cargo oil tank(COT) under various kinds of constraints in the preliminary design stage.A non-linear programming model is built to simulate the optimization design,in which the requirements and rules for COTD are used as the constraints.Considering the distance between the inner shell and hull,a fuzzy constraint is used to express the feasibility degree of the double-hull configuration.In terms of the characteristic of COTD,the PSO algorithm is improved to solve this problem.A bivariate extremum strategy is presented to deal with the fuzzy constraint,by which the maximum and minimum cargo capacities are obtained simultaneously.Finally,the simulation demonstrates the feasibility and effectiveness of the proposed approach.