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Combination of interval analysis and PSO for optimization

In this paper, a constrained optimization method for various functions such as non differentiable ones based on interval analysis is proposed. The process can be broken down into two distinct parts: the first one that approximates the space satisfying the constraints and the second one that is exclusively in charge of optimizing a given function. The first phase relies on successive bisections of the initial space while discarding the boxes that cannot verify the constraints. The last part of the algorithm is in charge of the unconstrained optimization using a Particle Swarm Optimization algorithm (commonly known as PSO).