Multiobjective Interacting Particle Algorithm for Global Optimization

We develop a population-based algorithm for the optimization of multiple, nonconvex, nondifferentiable, and possibly discontinuous objective functions. The algorithm employs Markov kernels, Hit-and-Run, and Pattern Hit-and-Run for exploration of the solution space and Pareto ordering rules for the selection of the population and to update the approximate Pareto optimal list. Our multiobjective interacting particle algorithm asymptotically converges to the stationary distribution associated with the Pareto ordering rules. We present numerical benchmark results on test problems.