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Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A meta-heuristic algorithm is a problem-independent technique that can be applied to a broad range of problems. In this experiment, some of the evolutionary algorithms will be tested, evaluated, and compared with each other. We will go through the Genetic Algorithm, Differential Evolution, Particle Swarm Optimization Algorithm, Grey Wolf Optimizer, and Simulated Annealing. They will be evaluated against the performance from many points of view like how the algorithm performs throughout generations and how the algorithm's result is close to the optimal result. Other points of evaluation are discussed in depth in later sections.

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In this paper, we consider a network game where players are multi-agent systems (we call them in this paper "coalitions") under the condition that the trajectories of players (coalitions) should (have no common arcs, or have no common vertices) i. e. must not intersect. In the same time the trajectories of players inside coalition can intersect (have common arcs,or have common vertices). The last condition complicates the problem, since the sets of strategies turn out to be mutually dependent. A family of Nash equilibrium is constructed and it is also shown that the minimum total time (cost) of players is achieved in a strategy profile that is a Nash equilibrium. A cooperative approach to solving the problem is proposed. Also, another cooperative mini maximal approach to solving the problem is investigated. We also consider the proportional solution and the Shapley value to allocate total minimal costs between players. Two approaches for constructing the characteristic function have been developed.