An optimization method for solving mixed discrete-continuous programming problems

This paper presents a heuristic approach for minimizing nonlinear mixed discrete-continuous problems with nonlinear mixed discrete-continuous constraints. The approach is an extension of the boundary tracking optimization that was developed by the authors to solve the minimum of nonlinear pure discrete programming problems with pure discrete constraints. The efficacy of the proposed approach is demonstrated by solving a number of test problems of the same class published in recent literature. Among these examples is the complex problem of minimizing the cost of a series–parallel structure with redundancies subject to reliability constraint. All tests conducted so far show that the proposed approach obtains the published minima of the respective test problems or finds a better minimum. While it is not possible to compare computation time due to the lack of data on the test problems, for all the tests the minimum is found in a reasonable time.