Generalized Dynamic Programming for Stochastic Combinatorial Optimization

In stochastic versions of combinatorial optimization problems, the objective is to maximize or minimize a function of random variables. For many problems of this type, conventionally applied dynamic programming DP may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of DP. We develop a generalization of DP that guarantees optimality even in the absence of monotonicity. We illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed DP algorithm E. Kao is potentially suboptimal due to the violation of monotonicity M. Sniedovich. Using Generalized DP, we are able to modify the algorithm to guarantee optimality.