# Balanced Team Formation Using Hybrid Graph Convolution Networks and MILP
## 1 Introduction  
Effective team building is crucial for successful projects. Research indicates that well-composed teams increase productivity, motivation, job satisfaction, and overall project outcomes [1]. This complex issue is relevant across a number of diverse fields, like education, healthcare, sports, and software development, wherever group work is necessary. However, teams often perform poorly despite individual efforts due to issues such as poor communication, conflict, ineffective knowledge sharing, ambiguous goals, and unclear roles. The team formation problem (TFP) is a challenging optimization problem focused on creating effective teams while considering numerous factors. The definition of \"effective\" varies based on context; some projects prioritize maximizing combined skills, while others focus on minimizing conflict or enhancing adaptability. Team composition can also vary depending on the task, with some favoring heterogeneous teams based on demographics, personality, or past performance, and others preferring homogeneous groups. The TFP's complexity increases with the pool of potential members and the number of constraints, making it computationally challenging (NP-hard). Various solutions exist, from simple brute-force methods to complex metaheuristics like Particle Swarm Optimization, Genetic Algorithms, and others. This research aims to categorize the most common optimization techniques used to solve the TFP based on their approach (exact, approximation, or hybrid) and application domain (e.g., education, sports, healthcare). Despite extensive research, a clear overview of the existing literature is lacking due to variations in the results obtained. This review synthesizes and evaluates the literature to highlight the most effective and frequently used techniques. These classifications will help professionals select appropriate algorithms for their projects based on their specific application domain. In addition, and appearing under various names, such as coalition structures (CSs), one can see that this topic has been extensively studied in terms of intelligent agents (IAs) [2, 3, 4]. Research on IAs aims to maximize the utility of both individual agents and teams (either the total team's utility or the average utility of each team member), specifically the likelihood of agents leaving their current group to join another. This problem, whether referred to as Team Formation (TFP) or Coalition Structure (CS) formation, remains NP-hard. However, of all the classifications of the algorithms proposed to solve the TFP, we have reached the conclusion that approximate algorithms constitute the largest group of techniques employed to address the team formation problem (TFP) due to their reduced computational demands. These algorithms prioritize finding a satisfactory solution rather than the absolute best. Typically non-deterministic and operating in polynomial time, they are favored when dealing with a large number of potential solutions. This category is broadly divided into heuristics and metaheuristics (MH). Metaheuristics are further classified into single-solution MH and population-based MH. Single-solution algorithms iteratively refine a single solution and aim to converge on a local optimum. These are suitable for single-team-formation scenarios. In contrast, population-based algorithms concurrently modify multiple solutions. As their convergence rate is generally slower than that of single-solution algorithms, they are better suited for problems involving the formation of multiple teams. Population-based techniques can be further subdivided into evolutionary algorithms (including the widely used Genetic Algorithm) and swarm-based or animal-inspired algorithms, such as Ant Colony Optimization (ACO), Bee Colony Optimization (BCO), and the Crow Search Algorithm (CSA). Finally, hybrid algorithms combine different approaches, such as exact methods and MHs, or two different MH techniques.