Genetic algorithms for discrete optimization and their applications to radio network design

Many radio network design problems can generally be formulated as discrete optimization problems. However, finding the optimal solution of a generic discrete optimization problem is NP-hard. In order to obtain a near-optimal solution within reasonable time, we propose to use genetic algorithms (GAs) and develop two search space reduction methods that can speed up their computation. The first method is to exploit the structure of the problem by encoding and manipulating solutions properly such that the structure constraints can be eliminated. We propose two approaches: (a) a genetic-fix algorithm (GA-FIX) that can generate and manipulate solutions with fixed size (i.e., in binary representation, the number of ones is fixed) and (b) a minimum-separation encoding scheme that can work with GA-FIX to maintain a minimum separation between consecutive elements in the solution. Analysis based on Markovian theory shows that GA-FIX converges asymptotically to the global optimum only when either eye or elitist strategy is added. We apply these approaches to solve both the channel assignment and the centralized broadcast scheduling problems and achieve substantial search space reduction. Simulations indicate that these approaches have significant improvement over some existing methods. The second method is to use implied objective function (IOF) constraints that bound the objective function of an optimization problem and hence, reduce the search space adaptively. Because the original optimality is not affected, these constraints can be used in any existing search algorithm. Using duality theory, we show that the dual problem with IOF constraint gives a tighter bound than that with conventional Lagrangean constructs. We apply this method to GAs for solving 0-1 integer programming problems. Simulations show that GAs with IOF constraint always out-perform the basic GA. Based on these methods, we devise a useful two-phase optimization routine that can solve any discrete constrained or unconstrained optimization problem. In addition, we develop a simulator which can implement genetic algorithms with the above concepts.