A new loading problem: product size reduction
Résumé
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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