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

Yuan Tian, Yi Mei+1 more|arXiv (Cornell University)|Jan 20, 2026

Resource-Constrained Project Scheduling0 citations

TL;DR

Introduces a knee-point based group selection mechanism within a multi-tree genetic programming framework to scale activity-group decisions in dynamic multi-mode resource-constrained project scheduling.

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.

Motivation & Objective

• Design a knee-point based group selection to limit candidate groups while preserving decision quality.
• Develop a multi-tree GP framework to evolve both an ordering rule and a group priority rule.
• Evaluate scalability and performance against sequential decision-making GP methods.

Proposed method

• Rank eligible activity-mode pairs with an ordering rule.
• Apply knee-point selection to identify promising pairs before group enumeration.
• Enumerate and prune activity groups from the knee-point filtered set within resource limits.
• Evolve both ordering and group-priority rules using a Koza-style multi-tree GP framework.
• Evaluate schedules by solving training instances and computing makespan lower-bound deviation.

Experimental results

Research questions

• RQ1 Can knee-point based filtering reduce the combinatorial blow-up in activity-group selection for DMRCPSP?
• RQ2 Do multi-tree GP-evolved ordering and group-priority rules outperform sequential decision-making GP?
• RQ3 How does knee-point guided group selection affect scalability and solution quality across varying precedence and resource complexities?

Key findings

• KGGP methods outperform sequential GP in most tested scenarios.
• Knee-point selection reduces candidate activity-mode pairs by a substantial margin, enabling larger problems to be tackled.
• Multi-tree GP can evolve both ordering and group-priority rules effectively.
• Rule analysis shows ordering rules favor urgent, resource-efficient pairs and group rules prefer quick groups with strong downstream impact.
• Training time increases with more complex precedence but KGGP remains scalable relative to fully enumerative methods.