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Simulated annealing for missile optimization: Developing method and formulation techniques

Hide-and-seek is a continuous simulated annealing algorithm that uses an adaptive cooling schedule. A number of improvements are proposed for the global optimum estimation required for the cooling schedule. To handle equality constraints, two approaches are examined: the rejection method and augmentation of constraints to cost using penalty coefficients. It is demonstrated that a faster convergence is possible if, in the penalty coefficients approach, equality constraints are replaced with tight inequality constraints. The missile trajectory optimization problem is formulated using nodes equally spaced in time until burnout and equally spaced in energy consumption after burnout. This approach is shown to be superior to the use of all nodes equally spaced in time. Also investigated is the effect of node number on the performance of the algorithm. The problem of combined optimization of design and control variables is also addressed. For this purpose a two-loop approach, where each loop has its own temperature and cooling schedule, is proposed, and its effectiveness is demonstrated.