Nature inspired genetic algorithms for hard packing problems

Abstract

This paper presents two novel genetic algorithms (GAs) for hard industrially relevant packing problems. The design of both algorithms is inspired by aspects of molecular genetics, in particular, the modular exon-intron structure of eukaryotic genes. Two representative packing problems are used to test the utility of the proposed approach: the bin packing problem (BPP) and the multiple knapsack problem (MKP). The algorithm for the BPP, the exon shuffling GA (ESGA), is a steady-state GA with a sophisticated crossover operator that makes maximum use of the principle of natural selection to evolve feasible solutions with no explicit verification of constraint violations. The second algorithm, the Exonic GA (ExGA), implements an RNA inspired adaptive repair function necessary for the highly constrained MKP. Three different variants of this algorithm are presented and compared, which evolve a partial ordering of items using a segmented encoding that is utilised in the repair of infeasible solutions. All algorithms are tested on a range of benchmark problems, and the results indicate a very high degree of accuracy and reliability compared to other approaches in the literature.

A grouping genetic algorithm with controlled gene transmission for the bin packing problem

“…The results that were obtained by this procedure are comparable to other results from more complex algorithms, such as HGGA and HI_BP [7,8]. Rohlfshagen and Bullinaria [19] developed a new genetic algorithm that was inspired by aspects of molecular genetics (ESGA). The authors compared their results with other state-of-the-art strategies, such as HI_BP and BISON [8,11], and obtained promising results.…”

“…GGA-CGT outperforms the results obtained by the state-of-the-art algorithms on the Hard28 set, which is the class of instances that were reported to date as the most difficult. The efficiency of the proposed algorithm is very high when compared to the number of iterations that are required by previous population strategies [7,15,16,18,19]. We are aware of the large number of parameters of GGA-CGT that must be estimated.…”

“…The initial population in most BPP evolutionary approaches is generally generated in a random manner by running a BPP heuristic on random permutations of the items [7,18,19]. Although we also generate random solutions, we first contribute to simplifying and improving the items' packing using a heuristic that is based on a dominance pattern that, given the set N of n items, determines the subset Ñ of ñ items that have weights that are larger than fifty percent of the bin capacity.…”

“…The mutation operator for BPP, which is encoded by the group-based scheme, has been defined differently [24]: given a chromosome, a few bins are eliminated from the solution; the items that composed those eliminated bins are thus missing from the solution, and they must be reinserted with some rearrangement heuristic. Usually, the selection of the bins to eliminate is made at random [7,19]; however, it has been noted that it is important to eliminate at least three bins and always eliminate the emptiest bin, to increase the probability of improving the solution quality [17,24]; we combine these two approaches.…”

“…Similar to most of the previous work on BPP [6,8], for each instance, a single execution of the algorithm GGA-CGT was run, with the initial seed for the random number generation set to 1. In all of the experiments, the following parameters were used for our GA implementation: The first two parameter values were established considering the values used by other GAs that solved BPP; they use a population size of 100 individuals and a maximum number of generations of between 1000 and 10,000 [7,17,19]. The other parameter values were tuned by means of an experimental approach [37] that was based on covering arrays to obtain a minimal representative set of sample configurations to assess the impact of the parameters that control the performance of the algorithm.…”