The Multi-Mode Resource Constraint Scheduling Problem is an NP-hard optimization problem. It arises in various industries such as construction engineering, transportation, and software development. This paper explores the integration of an adaptation of the Longest Processing Time heuristic to initialize the Variable State Independent Decaying Sum for the MRCPSP. This adaptation prioritizes tasks with a longer duration in all possible modes. Experimental evaluation demonstrates a 10% faster average computation time compared to default VSIDS, and the average deviation to the optimal solution is improved from 0.080% to 0.050%. These two findings combined show a minor improvement in using the LPT to initialize VSIDS values for the MRCPSP. Using the LPT also to initialize the default increment parameter, did not seem to yield any positive results.

This paper investigates the inclusion of domain-specific variable selection heuristics
in Constraint Programming (CP) solvers for the Prize-Collecting Job Sequencing
with One Common and Multiple Secondary Resources (PC-JSOCMSR) problem. We
propose two variable selection heuristics: a greedy variable selection method based on
densities, Highest Density First (HDF), and a modified Variable State Independent
Decaying Sum (VSIDS) initialized with job densities, referred to as VSIDS + Density.
Experimental results on benchmark instance sets reveal that the proposed heuristics
do not outperform the baseline VSIDS heuristic. Overall, they lead to higher conflict
counts and slower convergence. These findings highlight the robustness of generalpurpose
heuristics like VSIDS in diverse problem instances. Future research should
explore other domain-specific heuristics, as the current experiment demonstrates that
the proposed heuristics do not improve performance.