Intelligent Swap-Based Heuristics for Two-Objective Location Problems in Emergency Services

This scholarly article focuses on a specific application of discrete optimization methods in the emergency services. The search for the optimal deployment of service centers is one of the strategic decisions made in the field of urgent pre-hospital healthcare management. Since the consequences of the decisions are important for everyone and can directly affect the availability of the emergency medical service, different opinion groups are often taken into account when formulating a mathematical model. If there are two or more different conflicting objectives, the Pareto front of solutions usually needs to be constructed. It may serve as a good basis for finding the final system design. Since the construction of the exact Pareto set is very time-consuming and requires large computing resources, the efforts of many experts are focused on the development of efficient algorithms enabling the approximation of the original Pareto frontier in a short time. This paper introduces one of such heuristics. Even if the proposed algorithm of gradual refinement follows the idea of sequential processing of the current set of non-dominated solutions item by item inspecting the neighborhood of each element for possible extension of the Pareto front approximation, it can be simply adjusted and generalized making use of several parameters. Such an adjustment naturally raises the question of their optimal settings. Therefore, we gradually tried several procedures, from simple experimental verification of suitable values up to the development of sophisticated tuning of parameters based on machine learning methods. In this way, we created a complex advanced algorithm with elements of artificial intelligence. A series of numerical experiments are carried out utilizing real-world benchmarks that have their Pareto fronts applied in order to quantify and measure the efficacy of the proposed heuristic method.