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A new toolbox to optimize nonlinear objective functions by solving combinatorial problems in industrial applications

Anna Bassi & Manolo Venturin, Openeering/Enginsoft

Many industrial applications require the solution of a nonlinear optimization problem that can be reduced to the solution of a combinatorial problem. The developed toolbox optimizes the global efficiency (which is in general a nonlinear function) of a system composed of a certain number of machines of which the individual efficiency curves are known.

Our approach consists in approximating these curves with piecewise linear interpolation functions and in solving the efficiency problem for every configuration given by the combination of linear pieces of the curves approximations, (one piece for each machine). Each subproblem, given by a single configuration, is in general nonlinear, in spite of the linearity of the approximations. We solve the subproblems through an iterative method based on the linear approximation of the objective function. Since many configurations can give the same global efficiency, the solution is not unique. For this reason in the final report we list all the higher efficiency solutions, in order to let the user free to choose the best configuration according to other not modeled aspects.

The toolbox described in this work is completely developed in Scilab [1] and provided by Openeering [2]. Many of its facilities has been exploited, such as guis, file handling functions and the optimization toolbox. The toolbox, is user-friendly, even for inexperienced Scilab users.