[Paper Review] Surrogate-Assisted Genetic Programming with Rank-Based Phenotypic Characterisation for Dynamic Multi-Mode Project Scheduling

Yuan Tian, Yi Mei+1 more|arXiv (Cornell University)|Mar 17, 2026

Resource-Constrained Project Scheduling0 citations

TL;DR

Introduces a rank-based phenotypic characterisation for GP in DMRCPSP and integrates a nearest-neighbour surrogate to estimate fitness of unevaluated individuals, achieving faster discovery of high-quality scheduling heuristics.

ABSTRACT

The dynamic multi-mode resource-constrained project scheduling problem (DMRCPSP) is of practical importance, as it requires making real-time decisions under changing project states and resource availability. Genetic Programming (GP) has been shown to effectively evolve heuristic rules for such decision-making tasks; however, the evolutionary process typically relies on a large number of simulation-based fitness evaluations, resulting in high computational cost. Surrogate models offer a promising solution to reduce evaluation cost, but their application to GP requires problem-specific phenotypic characterisation (PC) schemes of heuristic rules. There is currently a lack of suitable PC schemes for GP applied to DMRCPSP. This paper proposes a rank-based PC scheme derived from heuristic-driven ordering of eligible activity-mode pairs and activity groups in decision situations. The resulting PC vectors enable a surrogate model to estimate the fitness of unevaluated GP individuals. Based on this scheme, a surrogate-assisted GP algorithm is developed. Experimental results demonstrate that the proposed surrogate-assisted GP can identify high-quality heuristic rules consistently earlier than the state-of-the-art GP approach for DMRCPSP, while introducing only marginal computational overhead. Further analyses demonstrate that the surrogate model provides useful guidance for offspring selection, leading to improved evolutionary efficiency.

Motivation & Objective

• Design a problem-specific phenotypic characterisation (PC) for GP heuristics in DMRCPSP based on ranking behaviour across decision situations.
• Develop a surrogate-assisted GP algorithm that uses the PC to estimate fitness and guide offspring selection.
• Demonstrate that the proposed SKGGP framework discovers high-quality heuristics earlier than the baseline KGGP with reduced evaluation cost.

Proposed method

• Represent GP individuals with two trees: an activity ordering rule and an activity group selection rule.
• Construct decision-situation-based PC vectors by ranking eligible candidates in each situation and concatenating these ranks.
• Use a nearest-neighbour surrogate in PC space to estimate fitness of unevaluated intermediate offspring.
• Generate k×|P| intermediate offspring per generation, keep unique PC vectors, estimate their fitness, and fully evaluate the top |P| offspring.
• Remove PC-duplicate individuals to focus evaluations on unique behavioural patterns.
• Compare SKGGP against KGGP across multiple DMRCPSP scenarios under five project instances each.

Experimental results

Research questions

• RQ1 Can a rank-based PC scheme faithfully capture GP behavioural differences in DMRCPSP decision contexts?
• RQ2 Does surrogate-assisted GP (SKGGP) reduce full fitness evaluations while maintaining or improving solution quality compared to KGGP?
• RQ3 How does the offspring multiplier k affect surrogate accuracy and evolutionary efficiency in DMRCPSP GP?
• RQ4 What is the overhead of introducing the surrogate model in terms of computation time and budget saved?
• RQ5 To what extent does surrogate-guided offspring selection accelerate convergence to high-quality heuristics?

Key findings

• SKGGP consistently outperforms KGGP when a larger number of intermediate offspring are generated (k=2 or 4).
• SKGGP achieves faster convergence than KGGP across all tested scenarios.
• With k=1, SKGGP can still improve over KGGP due to PC-based duplicate removal, but gains are magnified with higher k.
• Surrogate estimation adds modest overhead, accounting for roughly 1/20 to 1/40 of full evaluation time.
• Budget-saved analysis shows SKGGP reaches KGGP-equivalent quality with 20–40% fewer full evaluations.
• Surrogate precision in ranking top individuals decreases as k increases, indicating more challenging discrimination with larger candidate pools.