Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm

Abstract

In the present paper, we invoke a newly developed genetic hybrid algorithm (GHA) to solve the trim loss problem of a paper-converting mill. The genetic algorithm was specifically designed for nonconvex mixed integer nonlinear programming problems. The current problem is an integer non-convex nonlinear programming (INLP) problem involving bilinear constraints. As shown elsewhere, the problem can be written in expanded linear form and solved either as an integer linear programming (ILP) or as a mixed integer linear programming (MILP) problem. In each case, the formulation is a special case of MINLP and, therefore, directly solvable by the genetic hybrid algorithm. The example considered is taken from the family of real daily trim optimization problems encountered at a Finnish paper-converting mill with a yearly capacity of 100 000 t. In this paper, we present the genetic hybrid algorithm, the INLP-problem to be solved and compare the results with those obtained by a classical optimization method. Scope and purpose The purpose of this paper is to solve the trim loss problem encountered in the paper-converting industry using a newly developed genetic hybrid algorithm (GHA). The algorithm combines some key properties of genetic algorithms (GA) with classical constrained nonlinear mixed-integer programming methods. The greatest bottleneck of a paper-converting mill is the cutting of paper, due to the huge number of combinations needed in several kinds of product reels. In short, a poor cutting plane results in longer operation times, increased material consumption and, therefore, in increased waste production. The example considered is taken from the family of real daily trim optimization problems encountered at a Finnish paper-converting mill with a yearly capacity of 100 000 t. The problem is an integer non-convex nonlinear programming (INLP) problem involving bilinear constraints. As shown elsewhere, the problem can be written in expanded linear form and solved either as an integer linear programming (ILP) or as a mixed integer linear programming (MILP) problem. In each case, the formulation is a special case of MINLP and, therefore, directly solvable by the genetic hybrid algorithm. In this paper, we present the genetic hybrid algorithm, the INLP-problem to be solved and compare the results with those obtained by a recently developed optimization method based on classical optimization theory.