July  2017, 13(3): 1189-1211. doi: 10.3934/jimo.2016068

A multi-objective approach for weapon selection and planning problems in dynamic environments

1. 

College of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, China

2. 

Business School, Hunan University, Changsha 410082, Hunan, China

3. 

State Key Laboratory of Complex System Simulation, Beijing Institute of System Engineering, Beijing, China

4. 

College of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, China

* Corresponding author

Received  July 2015 Published  October 2016

Fund Project: The authors are supported by National Natural Science Foundation of China under Grants 71501181, 71401167, 71201169 and 71371067.

This paper addresses weapon selection and planning problems (WSPPs), which can be considered as an amalgamation of project portfolio and project scheduling problems. A multi-objective optimization model is proposed for WSPPs. The objectives include net present value (NPV) and effectiveness. To obtain the Pareto optimal set, a multi-objective evolutionary algorithm is presented for the problem. The basic procedure of NSGA-Ⅱ is employed. The problem-specific chromosome representation and decoding procedure, as well as genetic operators are redesigned for WSPPs. The dynamic nature of the planning environment is taken into account. Dynamic changes are modeled as the occurrences of countermeasures of specific weapon types. An adaptation process is proposed to tackle dynamic changes. Furthermore, we propose a flexibility measure to indicate a solution's ability to adapt in the presence of changes. The experimental results and analysis of a hypothetical case study are presented in this research.

Citation: Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068
References:
[1]

H. AbbassA. BenderH.H. DamS. BakerJ. Whitacre and R. Sarker, Computational scenario-based capability planning, Proceeding of GECCO'08, (2008), 1437-1444.  doi: 10.1145/1389095.1389378.  Google Scholar

[2]

K.P. Anagnostopoulos and G. Mamanis, A portfolio optimization model with three objectives and discrete variables, Computers & Operations Research, 37 (2010), 1285-1297.  doi: 10.1016/j.cor.2009.09.009.  Google Scholar

[3]

K.P. Anagnostopoulos and G. Mamanis, The mean-variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms, Expert Systems with Applications, 38 (2011), 14208-14217.  doi: 10.1016/j.eswa.2011.04.233.  Google Scholar

[4]

S. ArnoneA. Loraschi and A. Tettamanzi, A genetic approach to portfolio selection, Neural Network World, 3 (1993), 597-604.   Google Scholar

[5]

M. BarlowA. Yang and H.A. Abbass, A temporal risk assessment framework for planning a future force structure, Proceeding of CISDA 2007, (2007), 100-107.  doi: 10.1109/CISDA.2007.368141.  Google Scholar

[6]

J. BrankeB. ScheckenbachM. SteinK. Deb and H. Schmeck, Portfolio optimization with an envelope-based multi-objective evolutionary algorithm, European Journal of Operational Research, 199 (2009), 684-693.  doi: 10.1016/j.ejor.2008.01.054.  Google Scholar

[7]

J. Branke and D.C. Mattfeld, Anticipation and flexibility in dynamic scheduling, International Journal of Production Research, 43 (2005), 3103-3129.  doi: 10.1080/00207540500077140.  Google Scholar

[8]

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

[9]

A.F. CarazoaT. GómezJ. MolinaA.G. Hernández-DíazF.M. Guerrero and R. Caballero, Solving a comprehensive model for multiobjective project portfolio selection, Computers & Operations Research, 37 (2010), 630-639.  doi: 10.1016/j.cor.2009.06.012.  Google Scholar

[10]

T.-J. ChangN. MeadeJ.E. Beasley and Y.M. Sharaiha, Heuristics for cardinality constrained portfolio optimisation, Computers & Operations Research, 27 (2000), 1271-1302.  doi: 10.1016/S0305-0548(99)00074-X.  Google Scholar

[11]

W.-N. ChenJ. ZhangH.S.-H. ChungR.-Z. Huang and O. Liu, Optimizing discounted cash flows in project scheduling\-an ant colony optimization approach, IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 40 (2010), 64-77.   Google Scholar

[12]

S.V. deVonderE. Demeulemeester and W. Herroelen, A classification of predictive-reactive project scheduling procedures, Journal of Scheduling, 10 (2007), 195-207.  doi: 10.1007/s10951-007-0011-2.  Google Scholar

[13]

K. DebA. PratapS. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.   Google Scholar

[14]

K.U.B.R. N. Deb and S. Karthik, Dynamic multi-objective optimization and decision-making using modified nsga-ii: A case study on hydro-thermal power scheduling, Lecture Notes on Computer Science, 4403 (2007), 803-817.  doi: 10.1007/978-3-540-70928-2_60.  Google Scholar

[15]

K. DoernerW.J. GutjahrR.F. HartlC. Strauss and C. Stummer, Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection, Annals of Operations Research, 131 (2004), 79-99.  doi: 10.1023/B:ANOR.0000039513.99038.c6.  Google Scholar

[16]

P. Fox, A theory of cost-effectiveness for military systems analysis, Operations Research, 13 (1965), 191-201.  doi: 10.1287/opre.13.2.191.  Google Scholar

[17]

F. GhasemzadehN. Archer and P. Iyogun, A zero-one model for project portfolio selection and scheduling, Journal of Operations Research Society, 50 (1999), 745-755.   Google Scholar

[18]

B. GolanyM. KressM. Penn and U.G. Rothblum, Network optimization models for resource allocation in developing military countermeasures, Operations Research, 60 (2012), 48-63.  doi: 10.1287/opre.1110.1002.  Google Scholar

[19]

M.A. GreinerJ.W. FowlerD.L. ShunkW.M. Carlyle and R.T. McNutt, A hybrid approach using the analytic hierarchy process and integer programming to screen weapon systems projects, IEEE Transactions on Engineering Management, 50 (2003), 192-203.  doi: 10.1109/TEM.2003.810827.  Google Scholar

[20]

W.J. GutjahrS. KatzensteinerP. ReiterC. Stummer and M. Denk, Multi-objective decision analysis for competence-oriented project portfolio selection, European Journal of Operational Research, 205 (2010), 670-679.  doi: 10.1016/j.ejor.2010.01.041.  Google Scholar

[21]

M. Helbig and A.P. Engelbrecht, Analysing the performance of dynamic multi-objective optimisation algorithms, IEEE Congress on Evolutionary Computation, (2013), 1531-1539.  doi: 10.1109/CEC.2013.6557744.  Google Scholar

[22]

S. Hiromoto, Fundamental Capability Portfolio Management, PhD thesis, Pardee RAND Graduate School, 2013. Google Scholar

[23]

M.T. Jensen, Improving robustness and flexibility of tardiness and total flow time job shops using robustness measures, Applied Soft Computing, 1 (2001), 35-52.  doi: 10.1016/S1568-4946(01)00005-9.  Google Scholar

[24]

J. KangaspuntaJ. Liesiö and A. Salo, Cost-efficiency analysis of weapon system portfolios, European Journal of Operational Research, 223 (2012), 264-275.  doi: 10.1016/j.ejor.2012.05.042.  Google Scholar

[25]

T. KremmelJ. Kubalik and S. Biffl, Software project portfolio optimization with advanced multiobjective evolutionary algorithms, Applied Soft Computing, 11 (2011), 1416-1426.  doi: 10.1016/j.asoc.2010.04.013.  Google Scholar

[26]

J. LiesiöP. Mild and A. Salo, Robust portfolio modeling with incomplete cost information and project interdependencies, European Journal of Operational Research, 190 (2008), 679-695.  doi: 10.1016/j.ejor.2007.06.049.  Google Scholar

[27]

K. Metaxiotis and K. Liagkouras, Multiobjective evolutionary algorithms for portfolio management: A comprehensive literature review, Expert Systems with Applications, 39 (2012), 11685-11698.  doi: 10.1016/j.eswa.2012.04.053.  Google Scholar

[28]

D. Ouelhadj and S. Petrovic, A survey of dynamic scheduling in manufacturing systems, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1007/s10951-008-0090-8.  Google Scholar

[29]

A. PonsichA.L. Jaimes and C.A.C. Coello, A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications, IEEE Transactions on Evolutionary Computation, 17 (2013), 321-344.  doi: 10.1109/TEVC.2012.2196800.  Google Scholar

[30]

K. ShafiA. Bender and H.A. Abbass, Fleet estimation for defence logistics using a multi-objective learning classifier system, Proceeding of GECCO'11, (2011), 1195-1202.  doi: 10.1145/2001576.2001738.  Google Scholar

[31]

K. ShafiA. Bender and H.A. Abbass, Multi objective learning classifier systems based hyperheuristics for modularised fleet mix problem, Proceeding of SEAL 2012, 7673 (2012), 381-390.  doi: 10.1007/978-3-642-34859-4_38.  Google Scholar

[32]

F. StreichertH. Ulmer and A. Zell, Comparing discrete and continuous genotypes on the constrained portfolio selection problem, Genetic and Evolutionary Computation Conference, 3103 (2004), 1239-1250.  doi: 10.1007/978-3-540-24855-2_131.  Google Scholar

[33]

F. StreichertH. Ulmer and A. Zell, Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem, IEEE Congress on Evolutionary Computation, 1 (2004), 932-939.  doi: 10.1109/CEC.2004.1330961.  Google Scholar

[34]

H. Sun and T. Ma, A packing-multiple-boxes model for r & d project selection and scheduling, Technovation, 25 (2005), 1355-1361.  doi: 10.1016/j.technovation.2004.07.010.  Google Scholar

[35]

J.M. WhitacreH.A. AbbassR. SarkerA. Bender and S. Baker, Strategic positioning in tactical scenario planning, Proceeding of GECCO'08, (2008), 1081-1088.  doi: 10.1145/1389095.1389293.  Google Scholar

[36]

M. Workshop, Capabilities Based Planning: The Road Ahead, Technical report, Institute for Defense Analyses, Arlington, Verginia, 2004. Google Scholar

[37]

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

[38]

J. XiongK. wei YangJ. LiuQ. song Zhao and Y. wuChen, 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

[39]

S.-C. YangT.-L. LinT.-J. Chang and K.-J. Chang, A semi-variance portfolio selection model for military investment assets, Expert Systems with Applications, 38 (2011), 2292-2301.  doi: 10.1016/j.eswa.2010.08.017.  Google Scholar

[40]

E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach, IEEE Transactions on Evolutioanry Computation, 3 (1999), 257-271.  doi: 10.1109/4235.797969.  Google Scholar

show all references

References:
[1]

H. AbbassA. BenderH.H. DamS. BakerJ. Whitacre and R. Sarker, Computational scenario-based capability planning, Proceeding of GECCO'08, (2008), 1437-1444.  doi: 10.1145/1389095.1389378.  Google Scholar

[2]

K.P. Anagnostopoulos and G. Mamanis, A portfolio optimization model with three objectives and discrete variables, Computers & Operations Research, 37 (2010), 1285-1297.  doi: 10.1016/j.cor.2009.09.009.  Google Scholar

[3]

K.P. Anagnostopoulos and G. Mamanis, The mean-variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms, Expert Systems with Applications, 38 (2011), 14208-14217.  doi: 10.1016/j.eswa.2011.04.233.  Google Scholar

[4]

S. ArnoneA. Loraschi and A. Tettamanzi, A genetic approach to portfolio selection, Neural Network World, 3 (1993), 597-604.   Google Scholar

[5]

M. BarlowA. Yang and H.A. Abbass, A temporal risk assessment framework for planning a future force structure, Proceeding of CISDA 2007, (2007), 100-107.  doi: 10.1109/CISDA.2007.368141.  Google Scholar

[6]

J. BrankeB. ScheckenbachM. SteinK. Deb and H. Schmeck, Portfolio optimization with an envelope-based multi-objective evolutionary algorithm, European Journal of Operational Research, 199 (2009), 684-693.  doi: 10.1016/j.ejor.2008.01.054.  Google Scholar

[7]

J. Branke and D.C. Mattfeld, Anticipation and flexibility in dynamic scheduling, International Journal of Production Research, 43 (2005), 3103-3129.  doi: 10.1080/00207540500077140.  Google Scholar

[8]

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

[9]

A.F. CarazoaT. GómezJ. MolinaA.G. Hernández-DíazF.M. Guerrero and R. Caballero, Solving a comprehensive model for multiobjective project portfolio selection, Computers & Operations Research, 37 (2010), 630-639.  doi: 10.1016/j.cor.2009.06.012.  Google Scholar

[10]

T.-J. ChangN. MeadeJ.E. Beasley and Y.M. Sharaiha, Heuristics for cardinality constrained portfolio optimisation, Computers & Operations Research, 27 (2000), 1271-1302.  doi: 10.1016/S0305-0548(99)00074-X.  Google Scholar

[11]

W.-N. ChenJ. ZhangH.S.-H. ChungR.-Z. Huang and O. Liu, Optimizing discounted cash flows in project scheduling\-an ant colony optimization approach, IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 40 (2010), 64-77.   Google Scholar

[12]

S.V. deVonderE. Demeulemeester and W. Herroelen, A classification of predictive-reactive project scheduling procedures, Journal of Scheduling, 10 (2007), 195-207.  doi: 10.1007/s10951-007-0011-2.  Google Scholar

[13]

K. DebA. PratapS. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.   Google Scholar

[14]

K.U.B.R. N. Deb and S. Karthik, Dynamic multi-objective optimization and decision-making using modified nsga-ii: A case study on hydro-thermal power scheduling, Lecture Notes on Computer Science, 4403 (2007), 803-817.  doi: 10.1007/978-3-540-70928-2_60.  Google Scholar

[15]

K. DoernerW.J. GutjahrR.F. HartlC. Strauss and C. Stummer, Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection, Annals of Operations Research, 131 (2004), 79-99.  doi: 10.1023/B:ANOR.0000039513.99038.c6.  Google Scholar

[16]

P. Fox, A theory of cost-effectiveness for military systems analysis, Operations Research, 13 (1965), 191-201.  doi: 10.1287/opre.13.2.191.  Google Scholar

[17]

F. GhasemzadehN. Archer and P. Iyogun, A zero-one model for project portfolio selection and scheduling, Journal of Operations Research Society, 50 (1999), 745-755.   Google Scholar

[18]

B. GolanyM. KressM. Penn and U.G. Rothblum, Network optimization models for resource allocation in developing military countermeasures, Operations Research, 60 (2012), 48-63.  doi: 10.1287/opre.1110.1002.  Google Scholar

[19]

M.A. GreinerJ.W. FowlerD.L. ShunkW.M. Carlyle and R.T. McNutt, A hybrid approach using the analytic hierarchy process and integer programming to screen weapon systems projects, IEEE Transactions on Engineering Management, 50 (2003), 192-203.  doi: 10.1109/TEM.2003.810827.  Google Scholar

[20]

W.J. GutjahrS. KatzensteinerP. ReiterC. Stummer and M. Denk, Multi-objective decision analysis for competence-oriented project portfolio selection, European Journal of Operational Research, 205 (2010), 670-679.  doi: 10.1016/j.ejor.2010.01.041.  Google Scholar

[21]

M. Helbig and A.P. Engelbrecht, Analysing the performance of dynamic multi-objective optimisation algorithms, IEEE Congress on Evolutionary Computation, (2013), 1531-1539.  doi: 10.1109/CEC.2013.6557744.  Google Scholar

[22]

S. Hiromoto, Fundamental Capability Portfolio Management, PhD thesis, Pardee RAND Graduate School, 2013. Google Scholar

[23]

M.T. Jensen, Improving robustness and flexibility of tardiness and total flow time job shops using robustness measures, Applied Soft Computing, 1 (2001), 35-52.  doi: 10.1016/S1568-4946(01)00005-9.  Google Scholar

[24]

J. KangaspuntaJ. Liesiö and A. Salo, Cost-efficiency analysis of weapon system portfolios, European Journal of Operational Research, 223 (2012), 264-275.  doi: 10.1016/j.ejor.2012.05.042.  Google Scholar

[25]

T. KremmelJ. Kubalik and S. Biffl, Software project portfolio optimization with advanced multiobjective evolutionary algorithms, Applied Soft Computing, 11 (2011), 1416-1426.  doi: 10.1016/j.asoc.2010.04.013.  Google Scholar

[26]

J. LiesiöP. Mild and A. Salo, Robust portfolio modeling with incomplete cost information and project interdependencies, European Journal of Operational Research, 190 (2008), 679-695.  doi: 10.1016/j.ejor.2007.06.049.  Google Scholar

[27]

K. Metaxiotis and K. Liagkouras, Multiobjective evolutionary algorithms for portfolio management: A comprehensive literature review, Expert Systems with Applications, 39 (2012), 11685-11698.  doi: 10.1016/j.eswa.2012.04.053.  Google Scholar

[28]

D. Ouelhadj and S. Petrovic, A survey of dynamic scheduling in manufacturing systems, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1007/s10951-008-0090-8.  Google Scholar

[29]

A. PonsichA.L. Jaimes and C.A.C. Coello, A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications, IEEE Transactions on Evolutionary Computation, 17 (2013), 321-344.  doi: 10.1109/TEVC.2012.2196800.  Google Scholar

[30]

K. ShafiA. Bender and H.A. Abbass, Fleet estimation for defence logistics using a multi-objective learning classifier system, Proceeding of GECCO'11, (2011), 1195-1202.  doi: 10.1145/2001576.2001738.  Google Scholar

[31]

K. ShafiA. Bender and H.A. Abbass, Multi objective learning classifier systems based hyperheuristics for modularised fleet mix problem, Proceeding of SEAL 2012, 7673 (2012), 381-390.  doi: 10.1007/978-3-642-34859-4_38.  Google Scholar

[32]

F. StreichertH. Ulmer and A. Zell, Comparing discrete and continuous genotypes on the constrained portfolio selection problem, Genetic and Evolutionary Computation Conference, 3103 (2004), 1239-1250.  doi: 10.1007/978-3-540-24855-2_131.  Google Scholar

[33]

F. StreichertH. Ulmer and A. Zell, Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem, IEEE Congress on Evolutionary Computation, 1 (2004), 932-939.  doi: 10.1109/CEC.2004.1330961.  Google Scholar

[34]

H. Sun and T. Ma, A packing-multiple-boxes model for r & d project selection and scheduling, Technovation, 25 (2005), 1355-1361.  doi: 10.1016/j.technovation.2004.07.010.  Google Scholar

[35]

J.M. WhitacreH.A. AbbassR. SarkerA. Bender and S. Baker, Strategic positioning in tactical scenario planning, Proceeding of GECCO'08, (2008), 1081-1088.  doi: 10.1145/1389095.1389293.  Google Scholar

[36]

M. Workshop, Capabilities Based Planning: The Road Ahead, Technical report, Institute for Defense Analyses, Arlington, Verginia, 2004. Google Scholar

[37]

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

[38]

J. XiongK. wei YangJ. LiuQ. song Zhao and Y. wuChen, 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

[39]

S.-C. YangT.-L. LinT.-J. Chang and K.-J. Chang, A semi-variance portfolio selection model for military investment assets, Expert Systems with Applications, 38 (2011), 2292-2301.  doi: 10.1016/j.eswa.2010.08.017.  Google Scholar

[40]

E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach, IEEE Transactions on Evolutioanry Computation, 3 (1999), 257-271.  doi: 10.1109/4235.797969.  Google Scholar

Figure 1.  Chromosome representation
Figure 2.  A conceptual example of the adaptation process
Figure 3.  A conceptual example of the recovery process
Figure 4.  The whole adaptation procedure for each solution after dynamic changes occur
Figure 5.  Non-dominated set obtained with mutation rate 0.5 and crossover rates varying from 0.6 to 1.0
Figure 6.  Non-dominated sets obtained with crossover rate 0.7 and mutation rates varying from 0.1 to 0.6
Figure 7.  Convergence graph using hypervolume measure over time in 30 runs
Figure 8.  Comparison between non-dominated sets with and without the consideration of synergy effectiveness
Figure 9.  Behavior of the non-dominated set in the presence of dynamic changes
Figure 10.  Solutions in the presence of 1-4 dynamic changes without and after adaptation
Figure 11.  Solutions in the presence of 5-8 dynamic changes without and after adaptation
Figure 12.  A conceptual example of the calculation of adaptation effectiveness
Table 1.  Parameters of different type of weapons in the synthetical case
$w$ $a^{low}_{w}$ $a^{up}_{w}$ $c_w$ $d_w$ $r_w$
11540360
21030480
362010100
451012150
51220570
6816880
7818980
86151050
951513110
104818140
114815200
12416890
1351218150
1441016160
1561814120
1682012140
173818220
1851016180
193920180
207155100
$w$ $a^{low}_{w}$ $a^{up}_{w}$ $c_w$ $d_w$ $r_w$
11540360
21030480
362010100
451012150
51220570
6816880
7818980
86151050
951513110
104818140
114815200
12416890
1351218150
1441016160
1561814120
1682012140
173818220
1851016180
193920180
207155100
Table 2.  Parameters of dynamic environments
$No.$12345678
$w$104202175612
$t\_CW_w$2226283035485054
$No.$12345678
$w$104202175612
$t\_CW_w$2226283035485054
Table 3.  Correlation analysis between flexibility and adaptation in the presence of 8 changes
$No.$12345678
$corrcoef$0.85590.78920.54090.37970.32330.86630.79330.4643
$P-value$0.00000.00000.00000.00000.00000.00000.00000.0000
$No.$12345678
$corrcoef$0.85590.78920.54090.37970.32330.86630.79330.4643
$P-value$0.00000.00000.00000.00000.00000.00000.00000.0000
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