Scalable Knee-Point Guided Activity Group Selection in Multi-Tree Genetic Programming for Dynamic Multi-Mode Project Scheduling

TL;DR

This paper tackles dynamic multi-mode resource-constrained project scheduling with uncertain durations by evolving scheduling heuristics through a knee-point guided group selection within a multi-tree genetic programming framework. It simultaneously evolves an ordering rule for single activity-mode pairs and a group priority rule for evaluating activity groups, using knee-point filtering to prune candidate pairs before enumeration. The key contributions are the knee-point based filtering mechanism, the dual-rule multi-tree GP representation, and empirical evidence that KGGP outperforms sequential GP in large-scale instances while offering scalability benefits. The findings demonstrate practical improvements in real-time dynamic scheduling where considering groups of activities and resource interplay is beneficial, and they suggest broader applicability to complex, multi-resource scheduling problems.

Abstract

The dynamic multi-mode resource-constrained project scheduling problem is a challenging scheduling problem that requires making decisions on both the execution order of activities and their corresponding execution modes. Genetic programming has been widely applied as a hyper-heuristic to evolve priority rules that guide the selection of activity-mode pairs from the current eligible set. Recently, an activity group selection strategy has been proposed to select a subset of activities rather than a single activity at each decision point, allowing for more effective scheduling by considering the interdependence between activities. Although effective in small-scale instances, this strategy suffers from scalability issues when applied to larger problems. In this work, we enhance the scalability of the group selection strategy by introducing a knee-point-based selection mechanism to identify a promising subset of activities before evaluating their combinations. An activity ordering rule is first used to rank all eligible activity-mode pairs, followed by a knee point selection to find the promising pairs. Then, a group selection rule selects the best activity combination. We develop a multi-tree GP framework to evolve both types of rules simultaneously. Experimental results demonstrate that our approach scales well to large instances and outperforms GP with sequential decision-making in most scenarios.

Figures (9)

• Figure 1: Example project.
• Figure 2: Feasible schedule examples.
• Figure 3: Knee-point based group selection strategy.
• Figure 4: Convergence curves over 30 independent runs in six scenarios.
• Figure 5: Rule of evolved size in six scenarios over 30 independent runs.