Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model

Abstract

Novel deterministic heuristics are generated using Single Node Genetic Programming for application to the One Dimensional Bin Packing Problem. First a single deterministic heuristic was evolved that minimised the total number of bins used when applied to a set of 685 training instances. Following this, a set of heuristics were evolved using a form of cooperative co-evolution that collectively minimise the number of bins used across the same set of problems. Results on an unseen test set comprising a further 685 problem instances show that the single evolved heuristic outperforms existing deterministic heuristics described in the literature. The collection of heuristics evolved by cooperative co-evolution outperforms any of the single heuristics, including the newly generated ones.

Dual Inequalities for Stabilized Column Generation Revisited

“…As test instances we used the benchmark sets by Scholl et al (1997) and Sim and Hart (2013) comprising a total of 1,210 and 15,830 instances, respectively. Both benchmark sets are subdivided into several subclasses differing with respect to the number of items, the capacity, and the variance of the item weights resulting in instances with very different characteristics and degrees of complexity.…”

“…We further differentiate two subgroups for each of the benchmark sets: Groups 1 comprise the instances with computation times between one and ten seconds for aggregation, and it consist of 157 and 3,352 instances for the sets of Scholl et al (1997) and Sim and Hart (2013), respectively. The hardest instances in terms of solution time (> 10 seconds for aggregation) are in groups 2 consisting of the remaining 50 and 680 instances.…”

“…With a mix of statically and dynamically added DIs together with over-stabilization we gain another factor of approx. two for the extensive benchmark set of Sim and Hart (2013) and a factor of 2.5 for the widely used benchmark by Scholl et al (1997). Notably, while for this strategy (stat+dyn) the maximum slowdown was by factor 1.3, the maximum speedup was more than factor ten on some instances.…”

Mathematical models and decomposition algorithms for cutting and packing problems

“…Sim and Heart [261] used genetic programming as a generative hyper-heuristic to create deterministic heuristics.…”

CHAMP: Creating heuristics via many parameters for online bin packing

“…GP has been applied to many different challenging problems (Poli et al, 2008). Sim and Hart (2013) A particularly relevant study is provided in Burke et al (2006). The genetic programming approach is used to evolve heuristics to decide which bin to place a given item.…”