Applying Global Optimization to a Problem in Short-Term Hydrothermal Scheduling

Abstract

A method for modeling a real constrained optimization problem as a reverse convex programming problem has been developed from a new procedure of representation of a polynomial function as a difference of convex polynomials. An adapted algorithm, which uses a combined method of outer approximation and prismatical subdivisions, has been implemented to solve this problem. The solution obtained with a local optimization package is also included and their results are compared.

Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

“…In this section we report the numerical experiments we have made on some test problems by using our optimal d.c. representation together with the deterministic global optimization algorithm for solving reverse convex programming problems described in [4]. This algorithm combines a prismatical subdivision process with polyhedral outer approximation, in such a way that only linear programs have to be solved.…”

“…By using a prismatical subdivision process, this formulation allows for an advantageous adaptation of the combined outer approximation cone splitting conical algorithm for canonical d.c. programming as described in [4].…”

“…In the special case of polynomials, the problem of finding d.c. representations was addressed in [4].…”

Solving DC programs using the cutting angle method

“…Without this point these algorithms cannot work because the vertex of a conical subdivision process is needed. In this article we will use the prismatical algorithm (DCPA) described by Ferrer in [14], for comparing with DCECAM. DCPA though designed in a similar spirit to algorithms used for solving reverse convex programs, has several differences and advantages.…”

“…Horst and Tuy [17], Konno, Thach and Tuy [20], Tuy [27], Strekalovsky and Tsevendorj [26], An and Tao [22] and Ferrer [14] among others have put forward deterministic algorithms for solving DC programming problems whose nonconvexity is only due to having reverse convex constraints. All the mentioned algorithms combine conical or prismatical subdivision processes with polyhedral outer approximation in such a way that a finite number of linear programs have to be solved at each iteration.…”