Elsevier Editorial System(tm) for Computers & Operations Research Manuscript Draft Title: Multi-objective Metaheuristic Algorithms for the Resource- Constrained Project Scheduling Problem with Precedence Relations

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multi-objective Variable Neighborhood Search (MOVNS) and Pareto Iterated Local Search (PILS) methods. The proposed algorithms use strategies based on the concept of Pareto Dominance to search for solutions and determine the set of non-dominated solutions. The solutions obtained by the algorithms, from a set of instances adapted from the literature, are compared using four multi-objective performance measures: distance metrics, hypervolume indicator, epsilon metric and error ratio. The computational tests have indicated an algorithm based on MOVNS as the most efficient one, compared to the distance metrics; also, a combined feature of MOG and MOVNS appears to be superior compared to the hypervolume and epsilon metrics and one based on PILS compared to the error ratio. Statistical experiments have shown a significant difference between some proposed algorithms compared to the distance metrics, epsilon metric and error ratio. However, significant difference between the proposed algorithms with respect to hypervolume indicator was not observed.

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Alcione de Paiva Oliveira,et al.  Multi-objective Variable Neighborhood Search Algorithms for a Single Machine Scheduling Problem with Distinct due Windows , 2011, CLEI Selected Papers.

[3]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[4]  F. Kazemi.  Solving a multi-objective multi-mode resource-constrained project scheduling problem with discounted cash flows , 2011 .

[5]  Rainer Kolisch,et al.  PSPLIB - a project scheduling problem library , 1996 .

[6]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[7]  E. Kulinskaya,et al.  Power Approximations in Testing for Unequal Means in a One-Way ANOVA Weighted for Unequal Variances , 2003 .

[8]  Dalessandro Soares Vianna,et al.  A GRASP algorithm for the multi-criteria minimum spanning tree problem , 2008, Ann. Oper. Res..

[9]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[10]  Anurag Agarwal,et al.  A Neurogenetic approach for the resource-constrained project scheduling problem , 2011, Comput. Oper. Res..

[11]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[12]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[13]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[14]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[15]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[16]  Philipp Geyer,et al.  Component-oriented decomposition for multidisciplinary design optimization in building design , 2009, Adv. Eng. Informatics.

[17]  Saïd Salhi,et al.  A Tabu Search Approach for the Resource Constrained Project Scheduling Problem , 1998, J. Heuristics.

[18]  Martin Josef Geiger,et al.  Foundations of the Pareto Iterated Local Search Metaheuristic , 2008, ArXiv.

[19]  Roman Slowinski,et al.  Multiobjective project scheduling under multiple-category resource constraint , 1989 .

[20]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[21]  Rainer Kolisch,et al.  PSPLIB - A project scheduling problem library: OR Software - ORSEP Operations Research Software Exchange Program , 1997 .

[22]  Osman Oguz,et al.  A comparative study of computational procedures for the resource constrained project scheduling problem , 1994 .

[23]  Xavier Blasco Ferragud,et al.  Applied Pareto multi-objective optimization by stochastic solvers , 2009, Eng. Appl. Artif. Intell..

[24]  Michael Pilegaard Hansen,et al.  Tabu Search for Multiobjective Optimization: MOTS , 1997 .

[25]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[26]  Kerstin Vogler,et al.  Applications Of Multi Objective Evolutionary Algorithms , 2016 .

[27]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[28]  Beatriz de la Iglesia,et al.  A multi-objective GRASP for partial classification , 2008, Soft Comput..

[29]  Martin Josef Geiger,et al.  Randomised Variable Neighbourhood Search for Multi Objective Optimisation , 2008, ArXiv.

[30]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

[31]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[32]  Amir Abbas Najafi,et al.  Solving multi-mode resource-constrained project scheduling problem using two multi objective evolutionary algorithms , 2012 .

[33]  Rubén Ruiz,et al.  A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem , 2008, INFORMS J. Comput..

[34]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[35]  Kalyanmoy Deb,et al.  Running performance metrics for evolutionary multi-objective optimizations , 2002 .

[36]  Rosa Blanco,et al.  Theoretical and practical fundamentals for multi-objective optimisation in resource-constrained project scheduling problems , 2011, Comput. Oper. Res..

[37]  Shahram Shadrokh,et al.  Bi-objective resource-constrained project scheduling with robustness and makespan criteria , 2006, Appl. Math. Comput..

[38]  Jorge Pinho de Sousa,et al.  Using metaheuristics in multiobjective resource constrained project scheduling , 2000, Eur. J. Oper. Res..

[39]  Marcel Mongeau,et al.  Event-based MILP models for resource-constrained project scheduling problems , 2011, Comput. Oper. Res..

[40]  Mohamed Haouari,et al.  A bi-objective model for robust resource-constrained project scheduling , 2005 .

[41]  Rainer Kolisch.  Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation , 1994 .

[42]  Mehrdad Tamiz,et al.  Multi-objective meta-heuristics: An overview of the current state-of-the-art , 2002, Eur. J. Oper. Res..