Building General Hyper-Heuristics for Multi-Objective Cutting Stock Problems

In this article we build multi-objective hyperheuristics (MOHHs) using the multi-objective evolutionary algorithm NSGA-II for solving irregular 2D cutting stock problems under a bi-objective minimization schema, having a trade-off between the number of sheets used to fit a finite number of pieces and the time required to perform the placement of these pieces. We solve this problem using a multiobjective variation of hyper-heuristics called MOHH, whose main idea consists of finding a set of simple heuristics which can be combined to find a general solution, where a single heuristic is applied depending on the current condition of the problem instead of applying a unique single heuristic during the whole placement process. MOHHs are built after going through a learning process using the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We test the approximated MOHHs on several sets of benchmark problems and present the results.