Improving The Imperialist Competitive Algorithm To Find Nash Equilibrium Points In Crisis Management Problem



M.Sc. thesis

 In Information Technology Engineering

(Software Designing and Producing)





Problems that have several optimal points and all of that points help to solve it, is a multimodal optimization problem. In multimodal optimization, the user acquires more knowledge about different solutions for search space and it helps him to use another solution when this solution is not suitable for some reasons. The objective of the optimization techniques is maintaining diversity in the populations and between answer groups. also, the calculation of  Nash equilibrium points in non-cooperative multiplayer games is difficult. in games, when the number of players and their strategies and also game equilibrium points increases, mathematical algorithms are not able to identify all equilibrium points at a time because of difficulty in calculations. Evolutionary algorithms are a powerful search tool for solving these optimization problems.

The optimal allocation of resources to emergency locations in the event of multiple crises in an urban environment is an intricate problem, especially when the available resources are limited. In such a scenario, it is important to allocate emergency response units in a fair manner based on the criticality of the crisis events and their requests.

The Proposed algorithm, is improving the imperialist competitive algorithm to find Nash equilibrium points in crisis management problem. in this algorithm, optimums are searched in separate empires that are do this, we use an empire growth criterion for determining empire growth in development decades and then growing and unstable empires specifies, so the empires that evolved to a threshold  it means that it has an optimum so this optimum should save in the external storage, if an empire does not grow, that is unstable and it faces the revolution and will be demolished. after several algorithm iterations, saved answers in storage are all optimums of the problem.

In this thesis, The problem is formulated as a game-theoretic framework in which the crisis events are modeled as the players, the emergency response centers as the resource locations with emergency units to be Scheduled and the possible allocations as strategies.

In this problem we allocate some resources to each crisis , such that allocated resources to players (crisis) be the best possible combination and any other combination alter the situation to the worst status, these best combinations is not necessarily the same and they called Nash equilibrium points, we prove that the Lyapunov function return 0 for every such combination.

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