Abstract
Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many-objective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to different problem instances. We propose a methodology to exploit this characteristic by solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We use three goal-based objective functions and show that on benchmark instances of the multiobjective vehicle routing problem with time windows, the methodology is able to produce good results in short computation time. The methodology allows to combine the effectiveness of state-of-the-art multiobjective algorithms with the efficiency of goal programming to find good compromise solutions in problem scenarios where instances have similar fitness landscapes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Giagkiozis, I., Fleming, P.: Methods for many-objective optimization: an analysis. Research Report No. 1030 (2012)
Giagkiozis, I., Fleming, P.: Pareto front estimation for decision making. Evol. Comput. 22, 651–678 (2014)
Feliot, P., Bect, J., Vazquez, E.: A Bayesian approach to constrained single- and multi-objective optimization. J. Glob. Optim. 67(1–2), 97–133 (2017). https://link.springer.com/article/10.1007/s10898-016-0427-3
Toth, P., Vigo, D.: The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics (2002)
Pinheiro, R.L., Landa-Silva, D., Atkin, J.: Analysis of objectives relationships in multiobjective problems using trade-off region maps. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, GECCO 2015, pp. 735–742. ACM, New York (2015)
Pinheiro, R.L., Landa-Silva, D., Atkin, J.: A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems. J. Multi-Criteria Decis. Anal. 24, 37–56 (2017)
Pinheiro, R.L., Landa-Silva, D., Laesanklang, W., Constantino, A.A.: Using goal programming on estimated pareto fronts to solve multiobjective problems. In: Proceedings of the 7th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, INSTICC, pp. 132–143. SciTePress (2018)
Castro-Gutierrez, J., Landa-Silva, D., Moreno, P.J.: Nature of real-world multi-objective vehicle routing with evolutionary algorithms. In: IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 257–264 (2011)
Castro-Gutierrez, J., Landa-Silva, D., Moreno Perez, J.: Movrptw dataset (2015). https://github.com/psxjpc/ Accessed 24 Apr 2018
Charnes, A., Cooper, W.: Goal programming and multiple objective optimizations. Eur. J. Oper. Res. 1, 39–54 (1977)
Kornbluth, J.: A survey of goal programming. Omega 1, 193–205 (1973)
Jones, D., Tamiz, M.: A review of goal programming. In: Greco, S., Ehrgott, M., Figueira, J. (eds.) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, pp. 903–926. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-3094-4_21
Romero, C.: Titles of related interest. In: Handbook of Critical Issues in Goal Programming. Pergamon, Amsterdam (1991)
Tamiz, M., Jones, D.F., El-Darzi, E.: A review of goal programming and its applications. Ann. Oper. Res. 58, 39–53 (1995)
Flavell, R.B.: A new goal programming formulation. Omega 4, 731–732 (1976)
Jones, D., Tamiz, M.: Goal programming variants. In: Practical Goal Programming, pp. 11–22. Springer, Boston (2010). https://doi.org/10.1007/978-1-4419-5771-9_2
Tamiz, M., Mirrazavi, S., Jones, D.: Extensions of pareto efficiency analysis to integer goal programming. Omega 27, 179–188 (1999)
Hannan, E.: Nondominance in goal programming. INFOR Inf. Syst. Oper. Res. 18, 300–309 (1980)
Baykasoglu, A.: Preemptive goal programming using simulated annealing. Eng. Optim. 37, 49–63 (2005)
Mishra, S., Prakash, Tiwari, M.K., Lashkari, R.S.: A fuzzy goal-programming model of machine-tool selection and operation allocation problem in FMS: a quick converging simulated annealing-based approach. Int. J. Prod. Res. 44, 43–76 (2006)
Ghoseiri, K., Ghannadpour, S.F.: Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Appl. Soft Comput. 10, 1096–1107 (2010)
Leung, S.C.H.: A non-linear goal programming model and solution method for the multi-objective trip distribution problem in transportation engineering. Optim. Eng. 8, 277–298 (2007)
Azaiez, M.N., Al Sharif, S.S.: A 0-1 goal programming model for nurse scheduling. Comput. Oper. Res. 32, 491–507 (2005)
Musa, A.A., Saxena, U.: Scheduling nurses using goal-programming techniques. IIE Trans. 16, 216–221 (1984)
Calvete, H.I., Galé, C., Oliveros, M.J., Sánchez-Valverde, B.: A goal programming approach to vehicle routing problems with soft time windows. Eur. J. Oper. Res. 177, 1720–1733 (2007)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11, 712–731 (2007)
Bräysy, O., Gendreau, M.: Vehicle routing problem with time windows, Part II: metaheuristics. Transp. Sci. 39, 119–139 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Pinheiro, R.L., Landa-Silva, D., Laesanklang, W., Constantino, A.A. (2019). An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes. In: Parlier, G., Liberatore, F., Demange, M. (eds) Operations Research and Enterprise Systems. ICORES 2018. Communications in Computer and Information Science, vol 966. Springer, Cham. https://doi.org/10.1007/978-3-030-16035-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-16035-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16034-0
Online ISBN: 978-3-030-16035-7
eBook Packages: Computer ScienceComputer Science (R0)