Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems

Abstract

Abstract. This article presents a method based on the multi-objective evolutionary algorithm NSGA-II to approximate hyper-heuristics for solving irregular 2D cutting stock problems under multiple objectives. In this case, additionally to the traditional objective of minimizing the number of sheets used to fit a finite number of irregular pieces, the time required to perform the placement task is also minimized, leading to a bi-objective minimization problem with a tradeoff between the number of sheets and the time required for placing all pieces. We solve this problem using multi-objective hyper-heuristics (MOHHs), whose main idea consists of finding a set of simple heuristics which can be combined to find a general solution for a wide range of problems, 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. The MOHHs are approximated after going through a learning process by mean of the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We tested the approximated MMOHHs on several sets of benchmark problems, having outstanding results for most of the cases.

Choice function based hyper-heuristics for multi-objective optimization

“…MCHH has also been applied to real-world water distribution network design problems and has produced competitive results [41]. In [42], a new hyper-heuristic based on the multi-objective evolutionary algorithm NSGAII [8] is proposed. The main idea of this method is in producing the final Pareto-optimal set, through a learning process that evolves combinations of condition-action rules based on NSGAII.…”

A multi-objective hyper-heuristic based on choice function

“…None of the above have used multi-objective evolutionary algorithms (MOEAs), with the exception of (Gomez & Terashima-Marín, 2010;Vrugt & Robinson, 2007;Rafique, 2012) and none of the standard multi-objective test problems are studied, except in (McClymont & Keedwell, 2011;Vrugt & Robinson, 2007;Len et al, 2009;Vázquez-Rodríguez & Petrovic, 2013). Moreover, none of the previous hyper-heuristics make use of the components specifically designed for multi-objective optimization that we introduce.…”

Evolutionary multiobjective optimization: open research areas and some challenges lying ahead

“…Although the ideas behind hyper-heuristics can be traced back to the early 1960s in single-objective optimization, until relatively recently, their potential had not been explored in multiobjective optimization. Early attempts in this field date back to 2005, when hyper-heuristics started to be used to solve multiobjective combinatorial optimization problems, such as space allocation and timetabling [22], decision-tree induction algorithms [7], bin packing and cutting stock problems [59], integration and test order problems [63,64,107], spanning trees [89], job shop scheduling [162], knapsack problems [90] and software module clustering [91,92], among others.…”