Multi-Objective Differential Evolution with unbalanced Divide-and-Conquer Strategy for Warehouse Resource Allocation

Abstract

The Flexible Job Shop Scheduling Problem is well known as NP-hard and constrained. It is generic in the sense that many other problems are defined along similar lines. The Warehouse Resource Allocation problem belongs to this family, with its typically massive scale as an add-on factor. The severe non-concurrency constraint on both Tasks (Jobs) and Agents (Machines) remains valid. Here the problem is formulated in terms of the dual objectives of minimizing delay in completion of Tasks, and maximizing uniform utilization of available Agents. Differential Evolution (DE) is used for this multi-objective optimization, using both non-dominated sorting as well as variant linear combinations of multiple objectives. Efficacies of the two approaches are evaluated. The practical problem deals with thousands of Tasks represented as variables of the solution, which need to be loaded onto scores of Agents that appear as integer solutions of these variables. Since DE at basics is formulated to work on continuous spaces, here the integer solutions are mapped onto real spaces where DE is executed and then transformed back into integer space. Local Search is used to augment the baseline Global Search. A Divide-and-Conquer approach is implemented for the solution, with some novelty for handling variant, nonuniform sizes of different classes of Tasks and Agents.