Non-linear Multi-objective Optimization with Probabilistic Branch and Bound
This addresses computational efficiency in optimization for researchers and practitioners dealing with noisy, multi-objective problems, though it appears incremental as an extension of branch and bound methods.
The paper tackles stochastic multi-objective optimization by proposing MOPBnB(so), a simulation optimization algorithm that approximates Pareto optimal sets with single observations per solution, reducing computational intensity compared to a variant with multiple replications and outperforming NSGA-II on test problems.
A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier for stochastic multi-objective optimization problems. MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution to estimate the objective functions. A finite-time performance analysis for deterministic multi-objective problems provides a bound on the probability that MOPBnB(so) captures the Pareto optimal set. Asymptotic convergence of MOPBnB(so) on stochastic problems is derived, in that the algorithm captures the Pareto optimal set and the estimations converge to the true objective function values. Numerical results reveal that the variant with multiple replications is extremely intensive in terms of computational resources compared to MOPBnB(so). In addition, numerical results show that MOPBnB(so) outperforms a genetic algorithm NSGA-II on test problems.