Parallel Population Evolutionary Algorithms for the Time-Cost Trade-Off Relation Project Scheduling Problem

This research presents three approaches to solve multi-mode project scheduling problems with the objective of minimizing both project makespan and total cost. Total cost includes (1) total renewable resource investment for project executions; (2) activity mode execution cost including non-renewable resource consumption. The first approach applies a dual-population memetic algorithm (DPMA) within a double-loop, which consists of project deadline and renewable resource availability level. The second approach employs a double branch and bound method to find Pareto optimal solutions for cost and makespan. The third approach is a horizon varying two-phase method, which employs the minimization of total cost on a one-by-one basis for the deadlines within a pre-specified interval. Phase 1 of this approach uses a truncated branch and bound algorithm or shortest path method to construct an initial dual-population. Phase 2 applies a modified DPMA for evolution and further refinement. A comparative study is conducted via four benchmark instances drawn from PSPLIB. The experimental results indicate that the exact solution method is useful for small size problems with small resource factor values of both renewable and non-renewable types. The third approach is capable of producing near Pareto optimal solutions in a short time, and is not much affected by the resource factors.