Solving a new type of loading problem, the product size reduction, using a particle swarm optimization algorithm
François Schott  1, 2@  , Sébastien Salmon  2@  , Dominique Chamoret  3@  , Thomas Baron  4@  , Yann Meyer  5@  
1 : ED SPIM  -  Site web
EA 7274
1 rue Claude Goudimel - 25030 BESANCON -  France
2 : My-OCCS  -  Site web
my-occs
4J chemin de Palente 25000 Besançon -  France
3 : Laboratoire Interdisciplinaire Carnot de Bourgogne  (ICB)  -  Site web
CNRS : UMR6303, Université de Bourgogne
9 avenue Alain Savary, BP 47870, 21078 Dijon Cedex -  France
4 : Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies  (FEMTO-ST)  -  Site web
CNRS : UMR6174, Université de Franche-Comté, Université de Technologie de Belfort-Montbeliard, Ecole Nationale Supérieure de Mécanique et des Microtechniques
32 avenue de l'Observatoire 25044 BESANCON CEDEX -  France
5 : Laboratoire Mécatronique - Méthodes, Modèles et Métiers  (IRTES - M3M)  -  Site web
Institut de Recherche sur les Transports, l'Energie et la Société - IRTES, Université de Technologie de Belfort-Montbeliard
90010 Belfort cedex -  France

This paper introduces a new kind of cutting and loading problem: Product Size Reduction (PSR). This new kind of open dimension problems comes from the will of a company to reduce the size of an existing product, here a rack. The cutting and loading problems are widely studied as NP-hard problems. As they are closely related to each other, they can be sorted and solved by similar methods. The cutting and loading problems can be set by using different models, such as MILP or cuboid shape. To solve those problems, optimization algorithms, such as genetic algorithm, tree search and heuristics, are used. In addition, those algorithms may rely on positioning strategies, as for instance DBLF, layer building or anchor distance. Usually, the loading problems are focused on logistics problems as container or storage loading efficiency, whereas PSR problems are related to electronics, transport and energy industries. The aim of this work is to solve a real case 3D cuboid form PSR problem using a Particle Swarm Optimization (PSO) algorithm. This case differs from literature by two main features. First, all dimensions may vary between specific boundaries. Secondly, some objects have position constraints. A discrete space model has been built to represent the objects loading. As objects have position constraints, we chose to position them into space without using positioning strategies. The optimization process is based on waterfalls objective-functions. It is a different ways to take constraints into accounts, close to constraints relaxation and constraints ordering methods. Indeed, constraints are ordered and tested one after another. Depending on which constraints are fulfilled or not, a particular objective function is selected from a set. The PSO algorithm manages to find a solution reducing significantly the volume.


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