# Optimization of Warehouse Operations with Genetic Algorithms
## 5 The Proposed Method
### Data Format and Problem Encoding
The best results were obtained for the multiple restart genetic algorithm with AEX crossover operator (MR-AEX) for the product placement optimization process together genetic algorithm with multi-parent HGreX crossover operator (MP-HGreX) for order picking route optimization. The cost or route length caching can be used to accelerate the process. Additionally the Nearest Neighbor Algorithm can be used for route optimization to even more accelerate the process, but this is usually at the expense of a little worse result. In the future works we are planing to implement other modifications to further improve the speed of the optimization and the quality of the obtained solutions. First we want to evaluate new crossover operators and mixtures of various operators. In the experimental comparison of Puljic [19] the mix of different crossover operators performed slightly better than HGreX. Also more advanced mixes of genetic operators were proposed [35; 36]. However, we did not decide to use this approach because the implementation was definitely more complex. Instead we modified the HGreX to use multiple parents, what significantly improved the results. [PERSON] et al. [37] proposed the use of different operators (not only crossovers but also different mutations and other operators) for different individuals in standard genetic algorithms. We are going to adjust these approaches to the route and product placement optimizations and investigate various options. The other branch of our future research refers to constraints in the genetic algorithm operations as in some warehouses such constraints may exist and may limit the possible locations of particular products. In the literature the typical approach to constraints in genetic algorithms is the use of penalty functions [38]. Sometimes also dominance-based methods are used [39]. However, we are going to implement it differently by embedding the mechanism directly into the crossover and mutation operators specific to that problem in order to be able to enforce the constraint effectively and to limit the computational complexity of the optimization. Conceptualization, M.K. and S.G.; Formal analysis, M.B. and S.G.; Funding acquisition, M.B. and S.G.; Investigation, M.K. and J.B.; Methodology, M.K., S.G. and J.B.; Software, M.K. and J.B.; Validation, M.B. and S.G.; Visualization, M.B. and S.G.; Writing--original draft, M.K., J.B., M.B. and S.G. All authors have read and agreed to the published version of the manuscript. This work was supported by the Silesian University of Technology project: BK-204/2020/RM4. The authors want to thank [PERSON], [PERSON], [PERSON] and [PERSON] for their help in collecting and preparing the data used in this study. The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. ## References

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