This paper deals with multi- objective nonlinear programming problem having rough intervals in the constraints. The problem is approached by taking maximum value range and minimum value range inequalities as constraints conditions, reduces it into two classical multi-objective nonlinear programming problems, called lower and upper approximation problems.  All of the lower and upper approximatio...

Many engineering design problems involve a combination of both continuous anddiscrete variables. However, the number of studies scarcely exceeds a few on mixed-variableproblems. In this research Particle Swarm Optimization (PSO) algorithm is employed to solve mixedvariablenonlinear problems. PSO is an efficient method of dealing with nonlinear and non-convexoptimization problems. In this paper,...