Complementing Solutions for Facility Location Optimization via Video Game Crowdsourcing and Machine Learning Approach  
[PERSON]  
1 Department of Electrical Engineering, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Ciudad de Mexico 09340, Mexico; [EMAIL_ADDRESS] (M.V.-S.); [EMAIL_ADDRESS] (R.M.J.) [PERSON]  
2 Department of Applied Mathematics and Systems, Universidad Autonoma Metropolitana, Unidad Cuajalena, Ciudad de Mexico 0548, Mexico 20548  
scientific knowledge and has been used to solve problems for business, the public, and non-governmental sectors. The FLP is a common issue that frequently occurs in the fields of logistics and operations research. Despite its ubiquitousness, the complexity of the problem often renders obtaining optimal solutions for substantial instances within practical time limits challenging. For this reason, these problems are often tackled with heuristics [5], meta-heuristics, or stochastic approaches [6]. In particular, problems where a robust solution is needed--one that can endure a disruption and remain efficient--have been approached with genetic algorithms [7,8]. The aim of this study is to demonstrate the feasibility of incorporating human intuition and insight into solving complex problems such as the FLP, which frequently arise in logistics and operations research. The goal is to reduce transportation costs, enhance robustness in FLP, and allocate resources effectively. However, the task of acquiring knowledge from human participants is challenging due to the difficulty in articulating the thought processes that lead to a conclusion. People may have an intuitive sense of the solution to a particular problem instance, but their thought processes are not easily expressed in a concrete algorithm or heuristic. To address this challenge, a video game was employed to gather potential solutions from human participants. This game presents participants with multiple instances of optimization problems, aiming to aggregate their strategies into a unified algorithm or heuristic. The objective of this study is to demonstrate the feasibility of a hybrid human-computer approach in addressing challenging problems. A comparison between the results of this hybrid approach and traditional algorithmic methods, specifically genetic algorithms, was made concerning the facility location problem. No prior expertise or training is required for the human participants since the proposed video game is designed to be accessible to the general public. This study includes the design and implementation of a video game specifically for the FLP, as well as the data analysis and interpretation of the results obtained from individuals playing the game. While the widespread distribution of the game is not within the scope of this work, the game's design is intended to be suitable for such an objective, including the aim of increasing player engagement and gather more data per player. The design of the video game was intended to fulfill dual purposes, including providing basic training on the concepts of the problem and collecting candidate solutions. A critical aspect of the game design was that no prior knowledge or training was required to play and progress. This design choice was made for several reasons: to eliminate the costs and time associated with training participants beforehand; to ensure a broad distribution of the game to a large audience, which would be challenging to train individually; and to prevent the infusion of our own ideas, strategies, and assumptions related to the problem into the players since their unaltered perceptions and intuitions were the primary objective. In the existing literature, various approaches have been proposed to solve the FLP problem, including the use of heuristics, metaheuristics, and genetic algorithms [7, 8, 9, 10, 11]. Among these, genetic algorithms are the most widely used method. However, the computational resources and execution time required to apply genetic algorithms can be substantial.