Abstract-This study proposes a method for solving real-world warehouse Storage Location Assignment Problem (SLAP) under grouping constraints by Genetic Programming (GP). Integer Linear Programming (ILP) formulation is used to define the problem. By the proposed GP method, a subset of the items is repeatedly selected and placed into the available current best location of the shelves in the warehouse, until all the items have been assigned with locations. A heuristic matching function is evolved by GP to guide the selection of the subsets of items. Our comparison between the proposed GP approach and the traditional ILP approach shows that GP can obtain near-optimal solutions on the training data within a short period of time. Moreover, the evolved heuristics can achieve good optimization results on unseen scenarios, comparable to that on the scenario used for training. This shows that the evolved heuristics have good reusability and can be directly applied for slightly different scenarios without any new search process.

In this paper, a novel bi-level grouping optimization (BIGO) model is proposed for solving the storage location assignment problem with grouping constraint (SLAP-GC). A major challenge in this problem is the grouping constraint which restricts the number of groups each product can have and the locations of items in the same group. In SLAP-GC, the problem consists of two subproblems, one is how to group the items, and the other one is how to assign the groups to locations. It is an arduous task to solve the two subproblems simultaneously. To overcome this difficulty, we propose a BIGO. BIGO optimizes item grouping in the upper level, and uses the lower-level optimization to evaluate each item grouping. Sophisticated fitness evaluation and search operators are designed for both upper and lower level optimization so that the feasibility of solutions can be guaranteed, and the search can focus on promising areas in the search space. Based on the BIGO model, a multistart random search method and a tabu search algorithm are proposed. The experimental results on the real-world dataset validate the efficacy of the BIGO model and the advantage of the tabu search method over the random search method.

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The Storage Location Assignment Problem (SLAP) is a significant optimisation problem in warehouse management. Given a number of products, each with a set of items with different popularities (probabilities of being ordered), SLAP is to find the best locations for the items of the products in the warehouse to minimise the warehouse operational cost. Specifically, the operational cost is the expected cost of picking the orders. Grouping constraints are included to take the practical considerations into account in the problem. That is, the items belonging to the same product are more desirable to be placed together. In this paper, the SLAP with Grouping Constraints (SLAP-GC) is investigated, and an efficient Restricted Neighbourhood Tabu Search (RNTS) algorithm is proposed to solving it. RNTS adopts the problem-specific search operators to maintain solution feasibility, and the tabu list to prevent searching back and forth. RNTS was empirically compared with the mathematical programming method and a previously designed Genetic Programming method, which is demonstrated to be the state-of-the-art algorithm for SLAP-GC. The experimental results on the real-world data show that RNTS outperforms the stateof-the-art algorithms for SLAP-GC in terms of solution quality and speed. It managed to achieve optimal solutions for most of the small-scale instances much faster and outperformed the Genetic Programming method in terms of both solution quality and running time on all the test instances.

This study proposes a novel grammar guided Genetic Programming method to solve a real world problem, the Storage Location Assignment Problem (SLAP) with Grouping Constraints. Self-adaptive Tabu Search algorithms are evolved by this approach and it can be used as solvers for SLAPs. A novel self-adaptive Tabu Search framework is proposed that key configurations of the algorithm are determined based on the problem-specific characters, and these configurations are changed dynamically during the search process. In addition, both the quality of the solutions and the execution speed are considered in the evaluation function. The experimental results show that more efficient Tabu Search algorithms can be found by this approach comparing to a manually-designed Tabu Search method.