Adapting derivative free optimization methods to engineering models with discrete variables

In this paper we extend Continuous Derivative Free (CDF) algorithms that solve optimization models with continuous variables to the solution of optimization models with both continuous and discrete variables. The algorithm fits naturally to the solution of discretized models arising from continuous models. Roughly speaking, the finer the discretization, the closer the discretized solution is to its continuous counterpart. The algorithm also finds stationary points of real problems with continuous and discrete variables. Encouraging results are reported on an access point communication problem and on models solved with a Field Programmable Gate Array (FPGA) device, which generally forces a fixed point discretization of the problem.