An evolutionary search procedure for optimizing time–cost performance of projects under multiple renewable resource constraints

• The procedure can facilitate the interaction between the planning and scheduling phases.
• The processing mode can affect the requirement of activities.
• The procedure effectively strikes a balance between the cost and duration.
• A wide variety of performance measures can be handled.
• Based on the proposed methodology, many innovative techniques can be devised.

This paper presents an effective procedure for optimizing time–cost performance of multi-mode resource constrained project scheduling problems in which activities are subject to finish-start precedence constraints under renewable limited resources. Associated with each execution mode of activities, there exists a direct cost, a processing time, and a set of required renewable resources. In optimizing time–cost performance, the procedure treats the cost as a non-renewable resource whose limit can affect the duration of the project and balances cost versus time through the notion of priority-rank. This is performed by the use of a module which handles multimode projects, and since the procedure has to call this module with different limits on the cost, the effectiveness of this module plays a key role in the overall efficiency. For this reason, an effective evolutionary search technique has been developed to create the basis of this module. For testing its effectiveness, this module has been tested on 552 largest multimode benchmark instances of the PSPLIB and the results are promising: For over 98% of instances, the module finds the best available solutions in the literature. The module also produces a solution for one of these benchmark instances that is better than all of the current solutions in the literature.