Theory and Applications of Simulated Annealing for Nonlinear Constrained Optimization

Abstract

In this chapter, we present constrained simulated annealing (CSA), an algorithm that extendsconventional simulated annealing to look for constrained local minima of constrained optimiza-tion problems. The algorithm is based on the theory of extended saddle points (ESPs) thatshows the one-to-one correspondence between a constrained local minimum of the problem andan ESP of the corresponding penalty function. CSA finds ESPs by systematically controllingprobabilistic descents in the original variable space of the penalty function and probabilisticascents in the penalty space. Based on the decomposition of the necessary and sufficient ESPcondition into multiple necessary conditions, we also describe constraint-partitioned simulatedannealing (CPSA) that exploits the locality of constraints in nonlinear optimization problems.CPSA leads to much lower complexity as compared to that of CSA by partitioning the con-straints of a problem into exponentially simpler subproblems, solving each independently, andresolving those violated global constraints across the subproblems. We evaluate CSA and CPSAby applying them to solve some continuous constrained optimization problems and compare theirperformance to that of other penalty methods. Finally, we apply CSA to solve two real-worldapplications, one on sensor-network placement design and another on out-of-core compiler codegeneration.