Abstract
This paper deals with an optimization problem for a discrete-time system composed of a continuous subsystem and a discrete subsystem. The continuous subsystem has a continuous state and a continuous control. On the other hand, both the state and the control variables of the discrete subsystem are integers of the value 0 or 1. In addition, a constraint is introduced in order to represent the interactions between continuous and integer variables. In this problem, the performance index, the state equation and the constraint are assumed linear. Therefore, the problem treated here can be formulated as a mixed-integer linear program with staircase structure.
The purpose of this paper is to develop a decomposition method for solving mixed-integer linear programs with such special structure. The basic idea of the proposed algorithm is to decompose the problem in the same way as the Glassey's nested decomposition method in linear programs and to solve restricted master programs of mixed-integer type iteratively. A sufficient condition for optimality is obtained. Even if the procedure terminates without satisfying the optimality condition, at least a feasible solution is always obtained. Then, the proposed algorithm is expected to be efficient for finding a good suboptimal solution quickly. With an application to a dynamical planning problem of blending raw materials, it is observed that the algorithm requires less computing time than other methods.
