January  2017, 2(1): 39-58. doi: 10.3934/bdia.2017007

A moving block sequence-based evolutionary algorithm for resource investment project scheduling problems

Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi'an 710071, China

* Corresponding author: Jing Liu

Published  September 2017

Inspired by the representation designed for floorplanning problems, in this paper, we proposed a new representation, namely the moving block sequence (MBS), for resource investment project scheduling problems (RIPSPs). Since each activity of a project in RIPSPs has fixed duration and resource demand, we consider an activity as a rectangle block whose width is equal to the duration of the activity and height the resource needed by the activity. Four move modes are designed for activities, by using which the activity can move to the appropriate position. Therefore, the new representation of the project of RIPSPs consists of two parts: an activity list and a move mode list. By initializing the move modes randomly for each activity and moving it appropriately, the activity list can be decoded into valid solutions of RIPSPs. Since the decoding method of MBS guarantees that after moved, each activity is scheduled in the left-most and bottom-most position within a coordinate, which means that each activity in the corresponding project is arranged as early as possible when the precedence constraints and resource demands are satisfied. In addition, the multiagent evolutionary algorithm (MAEA) is employed to incorporate with the newly designed MBS representation in solving RIPSPs. With the intrinsic properties of MBS in mind, four behaviors, namely the crossover, mutation, competition, and self-learning operators are designed for agents in MAEA. To test the performance of our algorithm, 450 problem instances are used and the experimental results demonstrate the good performance of the proposed representation.

Citation: Xiaoxiao Yuan, Jing Liu, Xingxing Hao. A moving block sequence-based evolutionary algorithm for resource investment project scheduling problems. Big Data & Information Analytics, 2017, 2 (1) : 39-58. doi: 10.3934/bdia.2017007
References:
[1]

H. A. AbbassA. BenderH. DamS. BakerJ. M. Whitacre and R. A. Sarker, Computational scenario-based capability planning, in Genetic and Evolutionary Computation Conference (GECCO), ACM, Atlanta, Georgia, (2008), 1437-1444. doi: 10.1145/1389095.1389378. Google Scholar

[2]

P. BruckerA. DrexlR. MöhringK. Neumann and E. Pesch, Resource-constrained project scheduling: Notation, classification, models, and methods, European Journal of Operational Research, 112 (1999), 3-41. doi: 10.1016/S0377-2217(98)00204-5. Google Scholar

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L. T. BuiM. Barlow and H. A. Abbass, A multi-objective risk-based framework for mission capability planning, New Mathematics and Natural Computation, 5 (2009), 459-485. doi: 10.1142/S1793005709001428. Google Scholar

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F. ChicanoF. LunaA. J. Nebro and E. Alba, Using multi-objective metaheuristics to solve the software project scheduling problem, in GECCO'11 Proceedings of the 13th annual conference on Genetic and evolutionary computation, ACM, Dublin, Ireland, (2011), 1915-1922. doi: 10.1145/2001576.2001833. Google Scholar

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D. DebelsB. D. ReyckR. Leus and M. Vanhoucke, A hybrid scatter search/electromagnetism meta-heuristic for project scheduling, European Journal of Operational Research, 169 (2006), 638-653, Feature Cluster on Scatter Search Methods for Optimization. doi: 10.1016/j.ejor.2004.08.020. Google Scholar

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E. Demeulemeester, Minimizing resource availability costs in time-limited project networks, Management Science, 41 (1995), 1590-1598. doi: 10.1287/mnsc.41.10.1590. Google Scholar

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B. DepenbrockT. Balint and J. Sheehy, Leveraging design principles to optimize technology portfolio prioritization, in 2015 IEEE Aerospace Conference, (2015), 1-10. doi: 10.1109/AERO.2015.7119203. Google Scholar

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A. Drexl and A. Kimms, Optimization guided lower and upper bounds for the resource investment problem, The Journal of the Operational Research Society, 52 (2001), 340-351. doi: 10.1057/palgrave.jors.2601099. Google Scholar

[10]

K. S. HindiH. Yang and K. Fleszar, An evolutionary algorithm for resource-constrained project scheduling, IEEE Transactions on Evolutionary Computation, 6 (2002), 512-518. doi: 10.1109/TEVC.2002.804914. Google Scholar

[11]

R. Kolisch, Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation, European Journal of Operational Research, 90 (1996), 320-333. doi: 10.1016/0377-2217(95)00357-6. Google Scholar

[12]

R. Kolisch and S. Hartmann, Heuristic algorithms for the resource-constrained project scheduling problem: Classification and computational analysis, Project Scheduling, (1999), 147-178. doi: 10.1007/978-1-4615-5533-9_7. Google Scholar

[13]

R. Kolisch and S. Hartmann, Experimental investigation of heuristics for resource-constrained project scheduling: An update, European Journal of Operational Research, 174 (2006), 23-37. doi: 10.1016/j.ejor.2005.01.065. Google Scholar

[14]

R. KolischA. Sprecher and A. Drexl, Characterization and generation of a general class of resource-constrained project scheduling problems, Management Science, 41 (1995), 1693-1703. doi: 10.1287/mnsc.41.10.1693. Google Scholar

[15]

J. LiuW. Zhong and L. Jiao, A multiagent evolutionary algorithm for combinatorial optimization problems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40 (2010), 229-240. Google Scholar

[16]

J. LiuW. ZhongL. Jiao and X. Li, Moving block sequence and organizational evolutionary algorithm for general floorplanning with arbitrarily shaped rectilinear blocks, IEEE Transactions on Evolutionary Computation, 12 (2008), 630-646. Google Scholar

[17]

J. LiuW. Zhong and L. Jiao, A multiagent evolutionary algorithm for constraint satisfaction problems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36 (2006), 54-73. Google Scholar

[18]

L. L. MinkuD. Sudholt and X. Yao, Evolutionary algorithms for the project scheduling problem: runtime analysis and improved design, in GECCO'12 Proceedings of the 14th annual conference on Genetic and evolutionary computation, ACM, Philadelphia, Pennsylvania USA, (2012), 1221-1228. doi: 10.1145/2330163.2330332. Google Scholar

[19]

R. H. Möhring, Minimizing costs of resource requirements in project networks subject to a fixed completion time, Operational Research, 32 (1984), 89-120. Google Scholar

[20]

H. Nübel, The resource renting problem subject to temporal constraints, OR-Spektrum, 23 (2001), 359-381. doi: 10.1007/PL00013357. Google Scholar

[21]

C. Qian, Y. Yu and Z. -H. Zhou, Variable solution structure can be helpful in evolutionary optimization Science China Information Sciences, 58 (2015), 112105, 17 pp. doi: 10.1007/s11432-015-5382-y. Google Scholar

[22]

B. D. Reyck and R. Leus, R&d project scheduling when activities may fail, IIE Transactions, 40 (2008), 367-384. doi: 10.1080/07408170701413944. Google Scholar

[23]

S. R. Schultz and J. Atzmon, A simulation based heuristic approach to a resource investment problem (rip), in Proceedings of the Winter Simulation Conference, (2014), 3411-3422. doi: 10.1109/WSC.2014.7020174. Google Scholar

[24]

S. Shadrokh and F. Kianfar, A genetic algorithm for resource investment project scheduling problem, tardiness permitted with penalty, European Journal of Operational Research, 181 (2007), 86-101. doi: 10.1016/j.ejor.2006.03.056. Google Scholar

[25]

J. XiongJ. LiuY. Chen and H. A. Abbass, A knowledge-based evolutionary multiobjective approach for stochastic extended resource investment project scheduling problems, IEEE Transactions on Evolutionary Computation, 18 (2014), 742-763. Google Scholar

[26]

J. XiongK. wei YangJ. LiuQ. song Zhao and Y.wu. Chen, A two-stage preference-based evolutionary multi-objective approach for capability planning problems, Knowledge-Based Systems, 31 (2012), 128-139. doi: 10.1016/j.knosys.2012.02.003. Google Scholar

[27]

W. ZhongJ. LiuM. Xue and L. Jiao, A multiagent genetic algorithm for global numerical optimization, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34 (2004), 1128-1141. Google Scholar

show all references

References:
[1]

H. A. AbbassA. BenderH. DamS. BakerJ. M. Whitacre and R. A. Sarker, Computational scenario-based capability planning, in Genetic and Evolutionary Computation Conference (GECCO), ACM, Atlanta, Georgia, (2008), 1437-1444. doi: 10.1145/1389095.1389378. Google Scholar

[2]

P. BruckerA. DrexlR. MöhringK. Neumann and E. Pesch, Resource-constrained project scheduling: Notation, classification, models, and methods, European Journal of Operational Research, 112 (1999), 3-41. doi: 10.1016/S0377-2217(98)00204-5. Google Scholar

[3]

L. T. BuiM. Barlow and H. A. Abbass, A multi-objective risk-based framework for mission capability planning, New Mathematics and Natural Computation, 5 (2009), 459-485. doi: 10.1142/S1793005709001428. Google Scholar

[4]

F. ChicanoF. LunaA. J. Nebro and E. Alba, Using multi-objective metaheuristics to solve the software project scheduling problem, in GECCO'11 Proceedings of the 13th annual conference on Genetic and evolutionary computation, ACM, Dublin, Ireland, (2011), 1915-1922. doi: 10.1145/2001576.2001833. Google Scholar

[5]

S.-H. Cho and S. D. Eppinger, A simulation-based process model for managing complex design projects, IEEE Trans. Engineering Management, 52 (2005), 316-328. doi: 10.1109/TEM.2005.850722. Google Scholar

[6]

D. DebelsB. D. ReyckR. Leus and M. Vanhoucke, A hybrid scatter search/electromagnetism meta-heuristic for project scheduling, European Journal of Operational Research, 169 (2006), 638-653, Feature Cluster on Scatter Search Methods for Optimization. doi: 10.1016/j.ejor.2004.08.020. Google Scholar

[7]

E. Demeulemeester, Minimizing resource availability costs in time-limited project networks, Management Science, 41 (1995), 1590-1598. doi: 10.1287/mnsc.41.10.1590. Google Scholar

[8]

B. DepenbrockT. Balint and J. Sheehy, Leveraging design principles to optimize technology portfolio prioritization, in 2015 IEEE Aerospace Conference, (2015), 1-10. doi: 10.1109/AERO.2015.7119203. Google Scholar

[9]

A. Drexl and A. Kimms, Optimization guided lower and upper bounds for the resource investment problem, The Journal of the Operational Research Society, 52 (2001), 340-351. doi: 10.1057/palgrave.jors.2601099. Google Scholar

[10]

K. S. HindiH. Yang and K. Fleszar, An evolutionary algorithm for resource-constrained project scheduling, IEEE Transactions on Evolutionary Computation, 6 (2002), 512-518. doi: 10.1109/TEVC.2002.804914. Google Scholar

[11]

R. Kolisch, Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation, European Journal of Operational Research, 90 (1996), 320-333. doi: 10.1016/0377-2217(95)00357-6. Google Scholar

[12]

R. Kolisch and S. Hartmann, Heuristic algorithms for the resource-constrained project scheduling problem: Classification and computational analysis, Project Scheduling, (1999), 147-178. doi: 10.1007/978-1-4615-5533-9_7. Google Scholar

[13]

R. Kolisch and S. Hartmann, Experimental investigation of heuristics for resource-constrained project scheduling: An update, European Journal of Operational Research, 174 (2006), 23-37. doi: 10.1016/j.ejor.2005.01.065. Google Scholar

[14]

R. KolischA. Sprecher and A. Drexl, Characterization and generation of a general class of resource-constrained project scheduling problems, Management Science, 41 (1995), 1693-1703. doi: 10.1287/mnsc.41.10.1693. Google Scholar

[15]

J. LiuW. Zhong and L. Jiao, A multiagent evolutionary algorithm for combinatorial optimization problems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40 (2010), 229-240. Google Scholar

[16]

J. LiuW. ZhongL. Jiao and X. Li, Moving block sequence and organizational evolutionary algorithm for general floorplanning with arbitrarily shaped rectilinear blocks, IEEE Transactions on Evolutionary Computation, 12 (2008), 630-646. Google Scholar

[17]

J. LiuW. Zhong and L. Jiao, A multiagent evolutionary algorithm for constraint satisfaction problems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36 (2006), 54-73. Google Scholar

[18]

L. L. MinkuD. Sudholt and X. Yao, Evolutionary algorithms for the project scheduling problem: runtime analysis and improved design, in GECCO'12 Proceedings of the 14th annual conference on Genetic and evolutionary computation, ACM, Philadelphia, Pennsylvania USA, (2012), 1221-1228. doi: 10.1145/2330163.2330332. Google Scholar

[19]

R. H. Möhring, Minimizing costs of resource requirements in project networks subject to a fixed completion time, Operational Research, 32 (1984), 89-120. Google Scholar

[20]

H. Nübel, The resource renting problem subject to temporal constraints, OR-Spektrum, 23 (2001), 359-381. doi: 10.1007/PL00013357. Google Scholar

[21]

C. Qian, Y. Yu and Z. -H. Zhou, Variable solution structure can be helpful in evolutionary optimization Science China Information Sciences, 58 (2015), 112105, 17 pp. doi: 10.1007/s11432-015-5382-y. Google Scholar

[22]

B. D. Reyck and R. Leus, R&d project scheduling when activities may fail, IIE Transactions, 40 (2008), 367-384. doi: 10.1080/07408170701413944. Google Scholar

[23]

S. R. Schultz and J. Atzmon, A simulation based heuristic approach to a resource investment problem (rip), in Proceedings of the Winter Simulation Conference, (2014), 3411-3422. doi: 10.1109/WSC.2014.7020174. Google Scholar

[24]

S. Shadrokh and F. Kianfar, A genetic algorithm for resource investment project scheduling problem, tardiness permitted with penalty, European Journal of Operational Research, 181 (2007), 86-101. doi: 10.1016/j.ejor.2006.03.056. Google Scholar

[25]

J. XiongJ. LiuY. Chen and H. A. Abbass, A knowledge-based evolutionary multiobjective approach for stochastic extended resource investment project scheduling problems, IEEE Transactions on Evolutionary Computation, 18 (2014), 742-763. Google Scholar

[26]

J. XiongK. wei YangJ. LiuQ. song Zhao and Y.wu. Chen, A two-stage preference-based evolutionary multi-objective approach for capability planning problems, Knowledge-Based Systems, 31 (2012), 128-139. doi: 10.1016/j.knosys.2012.02.003. Google Scholar

[27]

W. ZhongJ. LiuM. Xue and L. Jiao, A multiagent genetic algorithm for global numerical optimization, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34 (2004), 1128-1141. Google Scholar

Figure 1.  An example of precedence graph
Figure 2.  An example of precedence graph
Figure 3.  The types of overlaps. (a) All kinds of top-overlaps, (b) all kinds of right-overlaps
Figure 4.  Relative positions of $CoverLeftX$ and $CoverRightX$. (a) and (b) are the cases without violating precedence constraints. (c) and (d) are the cases violating precedence constraints
Figure 5.  The decoding process
Figure 6.  The agent lattice of MBS$_{\rm {MAEA}}$-RIPSP
Table 1.  The Percentages of Finding Optimal Solutions for MBS$_{\rm MAEA}$-RIPSP on Möhring Instances with 1000 Evaluations
$C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
1/1/1/11.001.001.001.000.0670.033
3/1/1/11.000.900.900.800.1330.067
1/3/1/11.001.001.000.800.7000.333
1/1/3/11.001.001.001.000.9500.067
1/1/1/31.001.001.000.601.000.067
3/3/1/11.000.500.800.800.000.333
3/1/3/11.001.000.900.850.600.333
3/1/1/31.000.750.950.750.5330.067
1/3/3/11.001.001.001.000.700.033
1/3/1/31.001.001.001.000.800.00
1/1/3/31.001.001.001.000.600.00
3/3/3/11.001.000.901.000.3330.20
3/3/1/31.000.451.000.750.1330.033
3/1/3/31.001.000.950.850.1670.067
1/3/3/31.001.001.001.000.700.067
$C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
1/1/1/11.001.001.001.000.0670.033
3/1/1/11.000.900.900.800.1330.067
1/3/1/11.001.001.000.800.7000.333
1/1/3/11.001.001.001.000.9500.067
1/1/1/31.001.001.000.601.000.067
3/3/1/11.000.500.800.800.000.333
3/1/3/11.001.000.900.850.600.333
3/1/1/31.000.750.950.750.5330.067
1/3/3/11.001.001.001.000.700.033
1/3/1/31.001.001.001.000.800.00
1/1/3/31.001.001.001.000.600.00
3/3/3/11.001.000.901.000.3330.20
3/3/1/31.000.451.000.750.1330.033
3/1/3/31.001.000.950.850.1670.067
1/3/3/31.001.001.001.000.700.067
Table 2.  The Comparison of Numbers of Generation to Reach to the Optimal Solutions between MBS$_{\rm MAEA}$-RIPSP and GA for Möhring Test Sets
$C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
MBSGAMBSGAMBSGAMBSGAMBSGAMBSGA
1/1/1/111121116621141
3/1/1/111611212720271
1/3/1/1121331411243131
1/1/3/11111111112343
1/1/1/31111132112145
3/3/1/11112812125171
3/1/3/11111121181189
3/1/1/31212162198102
1/3/3/11111182111523
1/3/1/31112111186201
1/1/3/313131212537121
3/3/3/111121212914131
3/3/1/31141113288221
3/1/3/3121211121311845
1/3/3/3121213311934923
$C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
MBSGAMBSGAMBSGAMBSGAMBSGAMBSGA
1/1/1/111121116621141
3/1/1/111611212720271
1/3/1/1121331411243131
1/1/3/11111111112343
1/1/1/31111132112145
3/3/1/11112812125171
3/1/3/11111121181189
3/1/1/31212162198102
1/3/3/11111182111523
1/3/1/31112111186201
1/1/3/313131212537121
3/3/3/111121212914131
3/3/1/31141113288221
3/1/3/3121211121311845
1/3/3/3121213311934923
Table 3.  Parameter Settings for J10, J14 and J20 Test Sets
Test Set#AgentMaxGenExcuteNum$SelfLTime$$P_{cro}$$P_{mut}$$P_{com}$
J10$20\times 20$1010120.950.850.9
J14$20\times 20$108120.950.851.0
J20$20\times 19$108120.950.851.0
Test Set#AgentMaxGenExcuteNum$SelfLTime$$P_{cro}$$P_{mut}$$P_{com}$
J10$20\times 20$1010120.950.850.9
J14$20\times 20$108120.950.851.0
J20$20\times 19$108120.950.851.0
Table 4.  Experimental Results of MBS$_{\rm MAEA}$-RIPSP for J10, J14 and J20 Test Sets
$\theta$J10J14J20
Opt.%Dev.%Eva.Opt.%Dev.%Eva.Opt.%Dev.%Eva.
1.040.06.8896698876.50.7970371932.54.91267135
1.141.03.4006722563.01.0457498135.05.43357327
1.255.02.5922582143.1252.5851768333.04.92587273
1.351.52.4822617049.3752.2975736943.02.61737188
1.456.02.8036606547.51.9321677143.02.00797279
1.568.51.8743449655.01.8272746543.01.97287154
$\theta$J10J14J20
Opt.%Dev.%Eva.Opt.%Dev.%Eva.Opt.%Dev.%Eva.
1.040.06.8896698876.50.7970371932.54.91267135
1.141.03.4006722563.01.0457498135.05.43357327
1.255.02.5922582143.1252.5851768333.04.92587273
1.351.52.4822617049.3752.2975736943.02.61737188
1.456.02.8036606547.51.9321677143.02.00797279
1.568.51.8743449655.01.8272746543.01.97287154
Table 5.  Comparisons between MBS$_{\rm MAEA}$-RIPSP and GA for J10, J14 and J20 Test Sets
Test SetOpt.%Dev.%
MBSGAMBSGA
J1052.0048.203.34040.23
J1455.7540.001.74740.32
J2038.2533.333.64454.68
Test SetOpt.%Dev.%
MBSGAMBSGA
J1052.0048.203.34040.23
J1455.7540.001.74740.32
J2038.2533.333.64454.68
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