提出一种高效多目标优化算法，仅一次采样即可逼近最优解集。
Non-linear Multi-objective Optimization with Probabilistic Branch and Bound
- 基于单次观测的随机分支定界法，用邻近解估计目标函数。
- 理论证明有限时间内可捕获帕累托最优集，且渐近收敛于真实值。
- 相比多轮重复实验和遗传算法，计算效率更高，适合资源受限场景。
提出一种名为多目标概率分支定界带单次观测（MOPBnB(so)）的多目标仿真优化算法，用于近似求解随机多目标优化问题的帕累托最优集及其对应的有效前沿。该算法在任一解上仅需对噪声函数进行一次精确评估，并利用邻近解来估计目标函数值，与需在每个解上进行多次重复实验的变体形成对比。针对确定性多目标问题，给出了有限时间性能分析，提供了算法捕获帕累托最优集的概率上界。对于随机问题，推导出其渐近收敛性：算法能捕获帕累托最优集，且估计值收敛至真实目标函数值。数值结果表明，采用多次重复实验的变体在计算资源消耗上极为高昂，而MOPBnB(so)在测试问题上显著优于NSGA-II遗传算法。
原文摘要 · Abstract (English)
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.
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