Soft Comput DOI 10.1007/s00500-015-1606-8 METHODOLOGIES AND APPLICATION A model for resource-constrained project scheduling using adaptive PSO Neetesh Kumar · Deo Prakash Vidyarthi © Springer-Verlag Berlin Heidelberg 2015 Abstract Resource-constrained project scheduling prob- lem (RCPSP) is an important, but computationally hard prob- lem. 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. Con- ventional canonical PSO is improved at two points; during the particle’s position and velocity updation, due to depen- dent 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 par- ticle 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 (ω) 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 ω 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 prob- lems. Communicated by V. Loia. N. Kumar · D. P. Vidyarthi (B ) School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi 110067, India e-mail: dpv@mail.jnu.ac.in N. Kumar e-mail: dgoldneetesh15@gmail.com Keywords Particle swarm optimization · NP-hard · Heuristics · Resource-constrained project scheduling problem · Makespan 1 Introduction Resource-constrained project scheduling problem (RCPSP) is an important, but NP-hard problem in project planning research Blazewicz et al. (1983). Though, in the past, a num- ber of methods using linear programming, heuristics and meta-heuristics have been proposed to solve the RCPSP, these methods do not often produce good results and take substantial amount of time to converge. In recent times, researchers have intensified their interest towards optimal solution for RCPSP using evolved heuristics and meta- heuristics (Chen and Huang 2007; Valls et al. 2005) making this an active research area. RCPSP contains a set of activities with deterministic exe- cution time, precedence relation among activities, accumu- lative resources availability constraints and its consumption by the activities. The objectives in RCPSP is to find a feasible schedule with some quality characteristics such as optimal makespan and computation time, response time and through- put, such that all the constraints are satisfied. In literature, many exact scheduling algorithms to solve the RCPSP problem that uses linear programming approach (Pritsker et al. 1969; Kaplan 1996; Klein 2006; Mingozzi et al. 1998; Kone et al. 2011) are available. Out of these, the algorithms proposed by Brucker et al. (1998) and Mingozzi et al. (1998) seem to be the most effective and comprehen- sive. The drawback of their algorithms is that it solves the problem of small instances only (60 activities) in a satisfac- tory manner. Their method succumbs to higher convergence time for large instances as the solution search space increases 123