Soft Computing

, Volume 20, Issue 4, pp 1565–1580 | Cite as

A model for resource-constrained project scheduling using adaptive PSO

  • Neetesh Kumar
  • Deo Prakash Vidyarthi
Methodologies and Application


Resource-constrained project scheduling problem (RCPSP) is an important, but computationally hard problem. Particle swarm optimization (PSO) is a well-known and highly used meta-heuristics to solve such problems. In this work, a simple, effective and improved version of PSO i.e. adaptive-PSO (A-PSO) is proposed to solve the RCPSP. Conventional canonical PSO is improved at two points; during the particle’s position and velocity updation, due to dependent activities in RCPSP, a high possibility arises for the particle to become invalid. To overcome this, an important operator named valid particle generator (VPG) is proposed and embedded into the PSO which converts an invalid particle into a valid particle effectively with the knowledge of the in-degree and out-degree of the activities depicted by the directed acyclic graph. Second, inertia weight \((\omega )\) that plays a significant role in the quick convergence of the PSO is adaptively tuned by considering the effects of fitness value, previous value of \(\omega \) and iteration counter. Performance of the model is evaluated on the standard benchmark data of the RCPSP problem. Results show the effectiveness of the proposed model in comparison to other existing state of the art model that uses heuristics/meta-heuristics. The proposed model has the potential to be applied to other similar problems.


Particle swarm optimization NP-hard Heuristics  Resource-constrained project scheduling problem Makespan 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Computer and Systems SciencesJawaharlal Nehru UniversityNew DelhiIndia

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