This paper introduces a new approach to the Preemptive Resource Constrained Project Scheduling Problem with setup times. The method makes use of a Constraint Optimization Problem solver, which has been modified to use priority-rule-based heuristics in its variable and value selection procedures. An alternative implementation which uses a combination of a priority-rule heuristic and a domain-independent solver heuristic has also been investigated. Both methods were tested on four well-known problem sets against a problem-independent solver configuration. Experimental results show a significant reduction in the time needed to find optimal solutions for the new methods.

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.

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 looks at the different parts of the Critical Path and Resource Utilization (CPRU) heuristic for use in the Resource Constraint Project Scheduling Problem, with variable resources (RCPSP-t programming problem). RCPSP-t has many real-world instances such as in hospitals or manufacturing. Optimizing the solution generation for these instances may improve the efficiency of these industries. CPRU was split into parts and different versions were compared against VSIDS a more modern heuristic to determine if problem-specific heuristics perform better than generally good ones. A new adaptation of CPRU that adapts the research utilisation score by calculating the fraction used based on the amount of resources available given scheduled activities instead of looking at the resources of the problem instance. From the results, we concluded that CPRU may perform better for large instances of RCPSP- t compared to VSIDS in terms of generating good schedules within a few iterations. We also found that CPRU generates better schedules given a small time limit. We did not find evidence that the CPRU adaptation improved performance compared to CPRU in terms of schedule and time limits.