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This study proposes an optimal resource allocation algorithm of multiple UAVs with cooperative path planning using a geometric approach. The focus of the resource allocation is on mission and task completion, also known as feasibility whilst coping with operational and physical constraints of UAVs. Therefore, this study first introduces a geometric path planning algorithm based on Pythagorean Hodgraphs (PH). Using Bernstein Bzier polynomials, the path planning algorithm can generate feasible and safe (obstacle and inter-collision free) paths which can also meet position and orientation constraints of UAVs. We then optimise the resource allocation based on Evolutionary Game Particle Swarm Optimisation (EGPSO) and paths generated by the geometric planning. The input parameter of the optimal allocation problem is the allocation policy and the performance index is chosen to be the total flight time of the UAVs. Here the flight time is computed from the path produced by the path planning algorithm. The optimal allocation algorithm changes the allocation policy and finds the best allocation policy which minimise the performance index. The performance of the proposed algorithm is investigated by numerical examples simulated under realistic scenarios.