A New Repair Method For Constrained Optimization

Nowadays, constraints play an important role in industry, because most industrial optimization tasks underly several restrictions. Finding good solutions for a particular problem with respect to all constraint functions can be expensive, especially when the dimensionality of the search space is large and many constraint functions are involved. Unfortunately function evaluations in industrial optimization are heavily limited, because often expensive simulations must be conducted. For such high-dimensional optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of surrogate modeling for both the objective and the constraint functions. In this paper we present a new mechanism for COBRA to repair infill solutions with slightly violated constraints. The repair mechanism is based on gradient descent on surrogates of the constraint functions and aims at finding nearby feasible solutions. We test the repair mechanism on a real-world problem from the automotive industry and on other synthetic test cases. It is shown in this paper that with the integration of the repair method, the percentage of infeasible solutions is significantly reduced, leading to faster convergence and better final results.

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