An interactive heuristic approach can offer a practical solution to the problem of linear integer programming (LIP) by combining an optimization technique with the Decision Maker’s (DM) judgment and technical supervision. This is made possible using the concept of bicriterion linear programming (BLP) problem in an integer environment. This model proposes two bicriterion linear programs for iden...

Maximize ZD = b T y s.t. (D) A y + s = c, s ≥ 0n. where we have here chosen to add slack variables s ≥ 0n. The simplex method, as presented previously, works by starting with an initial basic feasible solution to (P) (which can be found via a phase 1 problem). However, what if a dual feasible basis is immediately available, whereas a basic feasible solution to (P) is harder to obtain? Can this ...

To understand how simplex solves a general linear programming problem, we need to know the answers to a number of questions: • How to determine if a minimum feasible solution has been found? • Which basic variable should become non-basic at a pivot step? • Which nonbasic variable is to enter the basis at a pivot step? • How to find an initial basic feasible solution to start simplex? We already...

an interactive heuristic approach can offer a practical solution to the problem of linear integer programming (lip) by combining an optimization technique with the decision maker’s (dm) judgment and technical supervision. this is made possible using the concept of bicriterion linear programming (blp) problem in an integer environment. this model proposes two bicriterion linear programs for iden...

This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses th...