Incorporating domain knowledge into Memetic Algorithms for solving Spatial Optimization problems

Spatial optimization problems (SOPs) are characterized by spatial relationships governing the decision variables, objectives and/or constraint functions. These are mostly combinatorial problems (NP-hard) due to the presence of discrete spatial units. Hence, exact optimization methods cannot solve them optimally under practical time constraints, especially for large-sized instances. Motivated by this challenge, we explore the use of population-based metaheuristics for solving SOPs. To this end, we observe that the search moves employed by these methods are suited to real-parameter continuous search space rather. To adapt them to the SOPs, we explore the role of domain knowledge in designing spatially-aware search operators that can efficiently search for an optimal solution in discrete search space while respecting the spatial constraints. These modifications result in a simple yet highly effective spatial hybrid metaheuristic called SPATIAL, which is applied to the problem of school boundary formation (also called school redistricting). Experimental findings on real-world datasets reveal the efficacy of our algorithm in obtaining superior quality solutions in comparison to traditional baseline methods. Additionally, we perform an in-depth study of the individual components of our framework and highlight the flexibility of our method in assimilating other search operators as well as in adapting it to related SOPs.