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Maximising the Net Present Value of Project Schedules Using CMSA and Parallel ACO

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Hybrid Metaheuristics (HM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11299))

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Abstract

This study considers the problem of resource constrained project scheduling to maximise the net present value. A number of tasks must be scheduled within a fixed time horizon. Tasks may have precedences between them and they use a number of common resources when executing. For each resource, there is a limit, and the cumulative resource requirements of all tasks executing at the same time must not exceed the limits. To solve this problem, we develop a hybrid of Construct, Merge, Solve and Adapt (CMSA) and Ant Colony Optimisation (ACO). The methods are implemented in a parallel setting within a multi-core shared memory architecture. The results show that the proposed algorithm outperforms the previous state-of-the-art method, a hybrid of Lagrangian relaxation and ACO.

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Notes

  1. 1.

    Note that, for consistency, the objective function value of an empty solution is defined as \(-\infty \).

  2. 2.

    Tasks are selected which have no preceding tasks first. This is followed by selecting dependent tasks that a free to be scheduled. This continues until all tasks have been scheduled.

  3. 3.

    http://www.gurobi.com/.

  4. 4.

    https://confluence.apps.monash.edu/display/monarch/MonARCH+Home.

  5. 5.

    https://www.sciencedirect.com/science/article/abs/pii/S0377221796001701.

  6. 6.

    Gurobi can solve most of the problem instances with 30 tasks (the optimal solutions are provided in PSPLIB), a number of instances with 60 tasks (\({<}60\%\)), and a very small proportion of the instances with 90 tasks (\({<}2\%\)). None of the instances with 120 tasks can be solved with Gurobi.

  7. 7.

    I is the set of instances.

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Acknowledgements

This research was supported in part by the Monash eResearch Centre and eSolutions-Research Support Services through the use of the MonARCH HPC Cluster.

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Melbourne, Australia

    Dhananjay Thiruvady & Andreas T. Ernst

  2. Artificial Intelligence Research Institute (IIIA-CSIC), Campus of the UAB, Bellaterra, Spain

    Christian Blum

Authors
  1. Dhananjay Thiruvady
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  2. Christian Blum
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  3. Andreas T. Ernst
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Corresponding author

Correspondence to Dhananjay Thiruvady .

Editor information

Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria J. Blesa Aguilera

  2. Spanish National Research Council, Bellaterra, Spain

    Christian Blum

  3. Universidade Federal de Ouro Preto, Ouro Preto, Brazil

    Haroldo Gambini Santos

  4. University of Concepción, Concepción, Chile

    Pedro Pinacho-Davidson

  5. Universidad de Concepción, Concepción, Chile

    Julio Godoy del Campo

A CMSA Parameter Selection

A CMSA Parameter Selection

In order to determine the parameter settings of CMSA for the experiments, a subset of the problem instances were selected and used for testing. The parameters of interest are the MIP time limit (we considered either 60 or 120 s), the number of ACO iterations (500, 1000 and 2000 iterations) and the maximum age limit (3, 5 and 10). The instances selected consist of 60 (small) and 120 (large) tasks, with resource factors of 0.5 (low-medium) and 1.0 (high), resource strengths of 0.5 (low-medium) and 1.0 (high). Each run was given 5 ACO colonies (and hence 5 cores) and 15 min of wall-clock time.

Table 3. Number of best solutions found by varying parameters (MIP time limit - MIP TL., ACO iterations - ACO iter. and Age limit - Age).
Full size table

Table 3 shows the number of instances for which the best solution was found with the respective settings. We consider the MIP time limit first, choose the best option, then select the best value for the number of ACO iterations, choose the best option, and finally select between the age limits. For the MIP time limit, 60 s is best for 60 and 120 tasks. Comparing iterations for 60 tasks, 500 is best and we use the same value for 120 tasks observing that there is no advantage. The best age limit for 120 tasks is 5, but because there is no obvious advantage for 60 tasks, we pick 3 in order for the built MIPs to be smaller and the MIP solver, therefore, faster.

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Thiruvady, D., Blum, C., Ernst, A.T. (2019). Maximising the Net Present Value of Project Schedules Using CMSA and Parallel ACO. In: Blesa Aguilera, M., Blum, C., Gambini Santos, H., Pinacho-Davidson, P., Godoy del Campo, J. (eds) Hybrid Metaheuristics. HM 2019. Lecture Notes in Computer Science(), vol 11299. Springer, Cham. https://doi.org/10.1007/978-3-030-05983-5_2

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  • DOI: https://doi.org/10.1007/978-3-030-05983-5_2

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  • Online ISBN: 978-3-030-05983-5

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