A simulated annealing technique for multi-objective simulation optimization

In this paper, we present a simulated annealing algorithm for solving multi-objective simulation optimization problems. The algorithm is based on the idea of simulated annealing with constant temperature, and uses a rule for accepting a candidate solution that depends on the individual estimated objective function values. The algorithm is shown to converge almost surely to an optimal solution. It is applied to a multi-objective inventory problem; the numerical results show that the algorithm converges rapidly. In many practical optimization problems, the evaluation of the objective function values is subject to noise, i.e., the objective function has no exact formula. This type of problem can be found in many complex stochastic systems. Simulation is the main tool used to estimate the performance of such systems. In this paper, we will consider the following discrete stochastic optimization problem: min h2H JðhÞ ¼ min E½hðh; Y h ފ ð1Þ where the feasible region H is the set of feasible solutions; h is the decision parameter consisting of the input parameters of the simulation; the objective function J : H ! R is the expected system performance when the input parameter values are given by h; and h is a deterministic, real-valued function that depends on h and on a random variable Y h that also depends on h. ފ is a real-valued function whose evaluation encounters some noise, then the problem becomes a multi-objective simulation problem for which an alternative that optimizes the vector J is desired. Of course, there may be no single h à that simultaneously minimizes all objectives. In this case, the various objectives are weighted by the decision maker and aggregated into a single objective optimization problem (see Weigert et al. [1]):