Abstract
This research investigates the pair formation problem described as forming pairs of people to achieve certain objectives. This problem is a subcategory of the well-known grouping problem that is classified as NP-complete. The necessity of pairing people in teams is frequent in many real-life fields such as education, social life, and production environments. To solve the problem, a mathematical formulation and a weighted graph-based representation are proposed. Pairing people is usually affected by psychological and productivity factors such as expertise and managers' opinion. These factors are summarised to produce quantitative scores representing the fitness relationship of each person towards others. Four algorithms are proposed to maximise the total weight of the formed pairs. The proposed algorithms are implemented and benchmarked using data instances of various sizes. The performance of the algorithms is evaluated against two proposed upper bounds. The results showed that the edge-based first algorithm (EPFA) outperforms other algorithms.
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