A random forest-guided hybrid evolutionary framework for stochastic multiobjective knapsack problems

The stochastic multi-objective knapsack problem (SMOKP) finds applications in critical fields such as logistics planning, resource allocation, and financial portfolio management. However, approximating the Pareto fronts (PFs) of SMOKPs poses significant challenges due to the high cost in the number of function evaluations when estimating expected objective function values under Monte Carlo sampling. While recent evolutionary algorithms (EAs) have improved the search efficiency of multi-objective optimization problems (MOPs), they often struggle with balancing sampling accuracy and computational budget in stochastic spaces within practical budgets, largely due to the sampling cost of uncertain parameters. To reduce the expense of function evaluations in sampling, this work proposes a novel random forest-guided hybrid evolutionary framework (SHMOEA-RF). The algorithm integrates three key innovations: (1) a hybrid search mechanism combining MOEA/D with dynamic weights and NSGA-II to maintain diversity; (2) a two-phase function evaluation strategy that first employs cheap single-sample evaluation followed by expensive multi-sample evaluations; and (3) random forest (RF) surrogate models that serve to approximate the expected function values, enabling the prediction of dominance, the selection of elite solutions, and the allocation of resources to promising areas. Computational experiments were conducted to evaluate the performance of SHMOEA-RF on both basic and expected-utility-based SMOKPs. The results demonstrate that SHMOEA-RF achieves superior performance in convergence and diversity compared with several baseline and state-of-the-art MOEAs, particularly in high-variance stochastic environments.