Robustness, stability, recoverability, and reliability in constraint satisfaction problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s10115-014-0778-3Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, which are addressed in engineering and other related areas.This work has been partially supported by the research project TIN2013-46511-C2-1 (MINECO, Spain). We would also thank the reviewers for their efforts and helpful comments.Barber Sanchís, F.; Salido Gregorio, MA. (2015). Robustness, stability, recoverability, and reliability in constraint satisfaction problems. Knowledge and Information Systems. 44(3):719-734. https://doi.org/10.1007/s10115-014-0778-3S719734443Abril M, Barber F, Ingolotti L, Salido MA, Tormos P, Lova A (2008) An assessment of railway capacity. Transp Res Part E 44(5):774–806Barber F (2000) Reasoning on intervals and point-based disjunctive metric constraints in temporal contexts. J Artif Intell Res 12:35–86Bartak R, Salido MA (2011) Constraint satisfaction for planning and scheduling problems. Constraints 16(3):223–227Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53Climent L, Wallace R, Salido M, Barber F (2013) Modeling robustness in CSPS as weighted CSPS. In: Integration of AI and OR techniques in constraint programming for combinatorial optimization problems CPAIOR 2013, pp 44–60Climent L, Wallace R, Salido M, Barber F (2014) Robustness and stability in constraint programming under dynamism and uncertainty. J Artif Intell Res 49(1):49–78Dechter R (1991) Temporal constraint network. Artif Intell 49:61–295Hazewinkel M (2002) Encyclopaedia of mathematics. Springer, New YorkHebrard E (2007) Robust solutions for constraint satisfaction and optimisation under uncertainty. PhD thesis, University of New South WalesHebrard E, Hnich B, Walsh T (2004) Super solutions in constraint programming. In: Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR-04), pp 157–172Jen E (2003) Stable or robust? What’s the difference? Complexity 8(3):12–18Kitano H (2007) Towards a theory of biological robustness. Mol Syst Biol 3(137)Liebchen C, Lbbecke M, Mhring R, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: LNCS, vol 5868Papapetrou P, Kollios G, Sclaroff S, Gunopulos D (2009) Mining frequent arrangements of temporal intervals. Knowl Inf Syst 21:133–171Rizk A, Batt G, Fages F, Solima S (2009) A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12):168–179Rossi F, van Beek P, Walsh T (2006) Handbook of constraint programming. Elsevier, New YorkRoy B (2010) Robustness in operational research and decision aiding: a multi-faceted issue. Eur J Oper Res 200:629–638Szathmary E (2006) A robust approach. Nature 439:19–20Verfaillie G, Schiex T (1994) Solution reuse in dynamic constraint satisfaction problems. In: Proceedings of the 12th national conference on artificial intelligence (AAAI-94), pp 307–312Wallace R, Grimes D, Freuder E (2009) Solving dynamic constraint satisfaction problems by identifying stable features. In: Proceedings of international joint conferences on artificial intelligence (IJCAI-09), pp 621–627Wang D, Tse Q, Zhou Y (2011) A decentralized search engine for dynamic web communities. Knowl Inf Syst 26(1):105–125Wiggins S (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, New YorkZhou Y, Croft W (2008) Measuring ranked list robustness for query performance prediction. Knowl Inf Syst 16:155–17

A Dual Scheduling Model for Optimizing Robustness and Energy Consumption in Manufacturing Systems

[EN] Manufacturing systems involve a huge number of combinatorial problems that must be optimized in an efficient way. One of these problems is related to task scheduling problems. These problems are NP-hard, so most of the complete techniques are not able to obtain an optimal solution in an efficient way. Furthermore, most of real manufacturing problems are dynamic, so the main objective is not only to obtain an optimized solution in terms of makespan, tardiness, and so on but also to obtain a solution able to absorb minor incidences/disruptions presented in any daily process. Most of these industries are also focused on improving the energy efficiency of their industrial processes. In this article, we propose a knowledge-based model to analyse previous incidences occurred in the machines with the aim of modelling the problem to obtain robust and energy-aware solutions. The resultant model (called dual model) will protect the more dynamic and disrupted tasks by assigning buffer times. These buffers will be used to absorb incidences during execution and to reduce the machine rate to minimize energy consumption. This model is solved by a memetic algorithm which combines a genetic algorithm with a local search to obtain robust and energy-aware solutions able to absorb further disruptions. The proposed dual model has been proven to be efficient in terms of energy consumption, robustness and stability in different and well-known benchmarks.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research has been supported by the Spanish Government under research project TIN2013-46511-C2-1 for the Spanish government and the TETRACOM EU project FP7-ICT-2013-10-No 609491.Escamilla Fuster, J.; Salido Gregorio, MA. (2016). A Dual Scheduling Model for Optimizing Robustness and Energy Consumption in Manufacturing Systems. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture. 1(1):1-12. https://doi.org/10.1177/0954405415625915S1121

Robustness, Stability, Recoverability and Reliability in Dynamic Constraint Satisfaction Problems

Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic, so that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency, and optimality have been the typical goals in the area, several is-sues regarding robustness appear with a clear relevance in dynamic constraint satisfaction problems (DCSPs). However, there is still no a clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability which arise in temporal DCSPs. All these definitions are based on related well-known concepts addressed in engineering and other related areas.Barber Sanchís, F.; Salido Gregorio, MA. (2011). Robustness, Stability, Recoverability and Reliability in Dynamic Constraint Satisfaction Problems. http://hdl.handle.net/10251/1070

Modelado y Resolución del Problema de Asignación de Horarios para el Transporte Ferroviario utilizando Técnicas de Satisfacción de Restricciones

El transporte ferroviario tiene un rol importante y creciente en muchos países, lo cual crea la necesidad de optimizar el uso de la infraestructura ferroviaria y los métodos y herramientas para su administración. La construcción de horarios ferroviarios es una tarea difícil que consume mucho tiempo, particularmente en el caso de redes ferroviarias reales. El objetivo del trabajo que se presenta, es realizar un modelado del problema de asignación de horarios para el trasporte ferroviario que permita aplicar las diferentes técnicas de resolución de programación de restricciones existentes en la literatura y evaluar su efectividad. El trabajo es de tipo descriptivo-documental bajo la modalidad de investigación básica. La metodología utilizada es del área de Inteligencia Artificial. Consiste en desarrollar una herramienta autómata que permita modelar instancias reales del problema como un Problema de Satisfacción de Restricciones (CSP); aplicar técnicas de solución y posteriormente evaluar los resultados. Se propone un modelado binario de CSP no-normalizado que contempla reglas de tráfico, requerimientos del usuario y reglas topológicas de una infraestructura real. Los resultados de las pruebas indican que en la búsqueda el algoritmo BLS tuvo un desempeño superior al 8Arangú, M.; Salido Gregorio, MA. (2014). Modelado y Resolución del Problema de Asignación de Horarios para el Transporte Ferroviario utilizando Técnicas de Satisfacción de Restricciones. Gestión y Gerencia. 8(2):45-64. http://hdl.handle.net/10251/80756S45648

Robustness, Stability, Recoverability and Reliability in CSP

Technical ReportMany real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise, and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency, and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, that are addressed in engineering and other related areas.Barber Sanchís, F.; Salido Gregorio, MA. (2013). Robustness, Stability, Recoverability and Reliability in CSP. http://hdl.handle.net/10251/2891

Robustness and Stability in Constraint Programming under Dynamism and Uncertainty

[EN] Many real life problems that can be solved by constraint programming, come from uncertain and dynamic environments. Because of the dynamism, the original problem may change over time, and thus the solution found for the original problem may become invalid. For this reason, dealing with such problems has become an important issue in the fields of constraint programming. In some cases, there is extant knowledge about the uncertain and dynamic environment. In other cases, this information is fragmentary or unknown. In this paper, we extend the concept of robustness and stability for Constraint Satisfaction Problems (CSPs) with ordered domains, where only limited assumptions need to be made as to possible changes. We present a search algorithm that searches for both robust and stable solutions for CSPs of this nature. It is well-known that meeting both criteria simultaneously is a desirable objective for constraint solving in uncertain and dynamic environments. We also present compelling evidence that our search algorithm outperforms other general-purpose algorithms for dynamic CSPs using random instances and benchmarks derived from real life problems.This work has been partially supported by the research project TIN2010-20976-C02-01 and FPU program fellowship (Min. de Ciencia e Innovacion, Spain). We wish to thank Dr. Christophe Lecoutre and Dr. Diarmuid Grimes for their assistance.Climent Aunés, LI.; Wallace, R.; Salido Gregorio, MA.; Barber Sanchís, F. (2014). Robustness and Stability in Constraint Programming under Dynamism and Uncertainty. Journal of Artificial Intelligence Research. 49(1):49-78. https://doi.org/10.1613/jair.4126S497849

Robust scheduling for Berth Allocation and Quay Crane Assignment Problem

[EN] Decision makers must face the dynamism and uncertainty of real-world environments when they need to solve the scheduling problems. Different incidences or breakdowns, for example, initial data could change or some resources could become unavailable, may eventually cause the infeasibility of the obtained schedule. To overcome this issue, a robust model and a proactive approach are presented for scheduling problems without any previous knowledge about incidences. This paper is based on proportionally distributing operational buffers among the tasks. In this paper, we consider the berth allocation problem and the quay crane assignment problem as a representative example of scheduling problems. The dynamism and uncertainty are managed by assessing the robustness of the schedules. The robustness is introduced by means of operational buffer times to absorb those unknown incidences or breakdowns. Therefore, this problem becomes a multiobjective combinatorial optimization problem that aims to minimize the total service time, to maximize the buffer times, and to minimize the standard deviation of the buffer times. To this end, a mathematical model and a new hybrid multiobjective metaheuristic is presented and compared with two well-known multiobjective genetic algorithms: NSGAII and SPEA2+.This work has been partially supported by by the Spanish Government under research project MINECO TIN2013-46511-C2-1-P, the project PIRSES-GA-2011-294931 (FP7-PEOPLE-2011-IRSES), and the predoctoral FPU fellowship (AP2010-4405).Rodríguez Molins, M.; Salido Gregorio, MA.; Barber Sanchís, F. (2014). Robust scheduling for Berth Allocation and Quay Crane Assignment Problem. Mathematical Problems in Engineering. 2014(1):1-17. https://doi.org/10.1155/2014/834927S11720141Imai, A., Chen, H. C., Nishimura, E., & Papadimitriou, S. (2008). The simultaneous berth and quay crane allocation problem. Transportation Research Part E: Logistics and Transportation Review, 44(5), 900-920. doi:10.1016/j.tre.2007.03.003Hu, Q.-M., Hu, Z.-H., & Du, Y. (2014). Berth and quay-crane allocation problem considering fuel consumption and emissions from vessels. Computers & Industrial Engineering, 70, 1-10. doi:10.1016/j.cie.2014.01.003Salido, M. A., Rodriguez-Molins, M., & Barber, F. (2011). Integrated intelligent techniques for remarshaling and berthing in maritime terminals. Advanced Engineering Informatics, 25(3), 435-451. doi:10.1016/j.aei.2010.10.001Rodriguez-Molins, M., Salido, M. A., & Barber, F. (2013). A GRASP-based metaheuristic for the Berth Allocation Problem and the Quay Crane Assignment Problem by managing vessel cargo holds. Applied Intelligence, 40(2), 273-290. doi:10.1007/s10489-013-0462-4Stahlbock, R., & Voß, S. (2007). Operations research at container terminals: a literature update. OR Spectrum, 30(1), 1-52. doi:10.1007/s00291-007-0100-9Lim, A. (1998). The berth planning problem. Operations Research Letters, 22(2-3), 105-110. doi:10.1016/s0167-6377(98)00010-8Bierwirth, C., & Meisel, F. (2010). A survey of berth allocation and quay crane scheduling problems in container terminals. European Journal of Operational Research, 202(3), 615-627. doi:10.1016/j.ejor.2009.05.031Kim, K. H., & Moon, K. C. (2003). Berth scheduling by simulated annealing. Transportation Research Part B: Methodological, 37(6), 541-560. doi:10.1016/s0191-2615(02)00027-9Giallombardo, G., Moccia, L., Salani, M., & Vacca, I. (2010). Modeling and solving the Tactical Berth Allocation Problem. Transportation Research Part B: Methodological, 44(2), 232-245. doi:10.1016/j.trb.2009.07.003Liang, C., Guo, J., & Yang, Y. (2009). Multi-objective hybrid genetic algorithm for quay crane dynamic assignment in berth allocation planning. Journal of Intelligent Manufacturing, 22(3), 471-479. doi:10.1007/s10845-009-0304-8Diabat, A., & Theodorou, E. (2014). An Integrated Quay Crane Assignment and Scheduling Problem. Computers & Industrial Engineering, 73, 115-123. doi:10.1016/j.cie.2013.12.012Park, Y.-M., & Kim, K. H. (2003). A scheduling method for Berth and Quay cranes. OR Spectrum, 25(1), 1-23. doi:10.1007/s00291-002-0109-zZhang, C., Zheng, L., Zhang, Z., Shi, L., & Armstrong, A. J. (2010). The allocation of berths and quay cranes by using a sub-gradient optimization technique. Computers & Industrial Engineering, 58(1), 40-50. doi:10.1016/j.cie.2009.08.002Lambrechts, O., Demeulemeester, E., & Herroelen, W. (2007). Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities. Journal of Scheduling, 11(2), 121-136. doi:10.1007/s10951-007-0021-0Hendriks, M., Laumanns, M., Lefeber, E., & Udding, J. T. (2010). Robust cyclic berth planning of container vessels. OR Spectrum, 32(3), 501-517. doi:10.1007/s00291-010-0198-zHan, X., Lu, Z., & Xi, L. (2010). A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time. European Journal of Operational Research, 207(3), 1327-1340. doi:10.1016/j.ejor.2010.07.018Xu, Y., Chen, Q., & Quan, X. (2011). Robust berth scheduling with uncertain vessel delay and handling time. Annals of Operations Research, 192(1), 123-140. doi:10.1007/s10479-010-0820-0Zhen, L., & Chang, D.-F. (2012). A bi-objective model for robust berth allocation scheduling. Computers & Industrial Engineering, 63(1), 262-273. doi:10.1016/j.cie.2012.03.003Blum, C., Puchinger, J., Raidl, G. R., & Roli, A. (2011). Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing, 11(6), 4135-4151. doi:10.1016/j.asoc.2011.02.032Ehrgott, M., & Gandibleux, X. (2008). Hybrid Metaheuristics for Multi-objective Combinatorial Optimization. Studies in Computational Intelligence, 221-259. doi:10.1007/978-3-540-78295-7_8Hanafi, R., & Kozan, E. (2014). A hybrid constructive heuristic and simulated annealing for railway crew scheduling. Computers & Industrial Engineering, 70, 11-19. doi:10.1016/j.cie.2014.01.002Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Kim, M., Hiroyasu, T., Miki, M., & Watanabe, S. (2004). SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2. Parallel Problem Solving from Nature - PPSN VIII, 742-751. doi:10.1007/978-3-540-30217-9_75Rodriguez-Molins, M., Ingolotti, L., Barber, F., Salido, M. A., Sierra, M. R., & Puente, J. (2014). A genetic algorithm for robust berth allocation and quay crane assignment. Progress in Artificial Intelligence, 2(4), 177-192. doi:10.1007/s13748-014-0056-3Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P. N., & Zhang, Q. (2011). Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation, 1(1), 32-49. doi:10.1016/j.swevo.2011.03.001Bandyopadhyay, S., Saha, S., Maulik, U., & Deb, K. (2008). A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA. IEEE Transactions on Evolutionary Computation, 12(3), 269-283. doi:10.1109/tevc.2007.900837While, L., Bradstreet, L., & Barone, L. (2012). A Fast Way of Calculating Exact Hypervolumes. IEEE Transactions on Evolutionary Computation, 16(1), 86-95. doi:10.1109/tevc.2010.207729

Rescheduling in job-shop problems for sustainable manufacturing systems

[EN] Manufacturing industries are faced with environmental challenges, so their industrial processes must be optimized in terms of both profitability and sustainability. Since most of these processes are dynamic, the previously obtained solutions cannot be valid after disruptions. This paper focuses on recovery in dynamic job-shop scheduling problems where machines can work at different rates. Machine speed scaling is an alternative framework to the on/off control framework for production scheduling. Thus, given a disruption, the main goal is to recover the original solution by rescheduling the minimum number of tasks. To this end, a new match-up technique is developed to determine the rescheduling zone and a feasible reschedule. Then, a memetic algorithm is proposed for finding a schedule that minimizes the energy consumption within the rescheduling zone but that also maintains the makespan constraint. An extensive study is carried out to analyze the behavior of our algorithms to recover the original solution and minimize the energy reduction in different benchmarks, which are taken from the OR-Library. The energy consumption and processing time of the tasks involved in the rescheduling zone will play an important role in determining the best match-up point and the optimized rescheduling. Upon a disruption, different rescheduling solutions can be obtained, all of which comply with the requirements but that have different values of energy consumption. The results proposed in this paper may be useful for application in real industries for energy-efficient production rescheduling.This research has been supported by the Seventh Framework Programme under the research project TETRACOM-GA609491 and the Spanish Government under research projects TIN2013-46511-C2-1, TIN2015-65515-C4-1-R and TIN2016-80856-R. The authors wish to thank reviewers and editors for their positive comments to improve the quality of the paper.Salido Gregorio, MA.; Escamilla Fuster, J.; Barber Sanchís, F.; Giret Boggino, AS. (2017). Rescheduling in job-shop problems for sustainable manufacturing systems. Journal of Cleaner Production. 162(20):121-132. https://doi.org/10.1016/j.jclepro.2016.11.002S1211321622

PSPLIB-ENERGY: Una extension de la libreria PSPLIB para la evaluacion de la optimizacion energetica en el RCPSP

[EN] Scheduling problems is one of the core areas in the planning and development of any project, with a wide applicability to real-world situations. Due to the high complexity of these problems, the solving process is often based on metaheuristics techniques, so that the evaluation of these methods is empirical. Therefore benchmarks, which provide a set of test cases to assess the behavior of algorithms, are generated. This paper extends the PSPLIB library. This extension incorporates to each instance of RCPSP (Resource Constrained Project Scheduling Problem), a realistic mathematical model of energy consumption. This proposal provides an alternative to the current trend in the feld of optimization and manufacturing that requires the inclusion of components and methods that reduce the environmental impact in the process of decision making. Finally a new optimality criterion is proposed to compare dierent search techniques. The PSPLIB-ENERGY is available at http://gps.webs.upv.es/psplib-energy/[ES] Los problemas de scheduling constituyen una de las ´areas centrales en la planificaci´on y desarrollo de cualquier proyecto, con una gran aplicabilidad a situaciones del mundo real. Debido a la gran complejidad que habitualmente presentan estos problemas, su resoluci´on suele basarse en m´etodos metaheur´ısticos de optimizaci´on, de forma que la evaluaci´on de estos m´etodos es emp´ırica. Por esta raz´on se generan benchmarks, que proveen de un conjunto de casos de prueba que permiten evaluar el comportamiento de los algoritmos que se desarrollan. En este art´ıculo se extiende la librer´ıa PSPLIB. Esta extensi´on consiste en incorporar a cada instancia del RCPSP (Resource Constrained Project Scheduling Problem), un modelo matem´atico realista de consumo de energ´ıa. Esta propuesta brinda una alternativa a la tendencia actual en el campo de la optimizaci´on y la manufactura que demanda la inclusi´on de componentes y m´etodos que reduzcan el impacto ambiental en el proceso de toma de decisiones. Finalmente se propone un nuevo criterio de optimalidad para comparar las diferentes t´ecnicas de b´usqueda. La PSPLIB-ENERGY est´a disponible en http://gps.webs.upv.es/psplib-energy/.Este trabajo ha sido parcialmente financiado por el proyecto de Investigación TIN2013-46511-C2-1-P.Morillo Torres, D.; Barber Sanchís, F.; Salido Gregorio, MA. (2014). PSPLIB-ENERGY: Una extension de la libreria PSPLIB para la evaluacion de la optimizacion energetica en el RCPSP. Inteligencia Artificial. Revista Iberoamericana de Inteligencia Artificial. 17(54):35-48. https://doi.org/10.4114/intartif.vol17iss54pp48-61S3548175

A New Optimization Algorithm Based on Search and Rescue Operations

[EN] In this paper, a new optimization algorithm called the search and rescue optimization algorithm (SAR) is proposed for solving single-objective continuous optimization problems. SAR is inspired by the explorations carried out by humans during search and rescue operations. The performance of SAR was evaluated on fifty-five optimization functions including a set of classic benchmark functions and a set of modern CEC 2013 benchmark functions from the literature. The obtained results were compared with twelve optimization algorithms including well-known optimization algorithms, recent variants of GA, DE, CMA-ES, and PSO, and recent metaheuristic algorithms. The Wilcoxon signed-rank test was used for some of the comparisons, and the convergence behavior of SAR was investigated. The statistical results indicated SAR is highly competitive with the compared algorithms. Also, in order to evaluate the application of SAR on real-world optimization problems, it was applied to three engineering design problems, and the results revealed that SAR is able to find more accurate solutions with fewer function evaluations in comparison with the other existing algorithms. Thus, the proposed algorithm can be considered an efficient optimization method for real-world optimization problems.This study was partially supported by the Spanish Research Project (nos. TIN2016-80856-R and TIN2015-65515-C4-1-R).Shabani, A.; Asgarian, B.; Gharebaghi, SA.; Salido Gregorio, MA.; Giret Boggino, AS. (2019). A New Optimization Algorithm Based on Search and Rescue Operations. Mathematical Problems in Engineering. 2019:1-23. https://doi.org/10.1155/2019/2482543S1232019Bianchi, L., Dorigo, M., Gambardella, L. M., & Gutjahr, W. J. (2008). A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8(2), 239-287. doi:10.1007/s11047-008-9098-4Holland, J. H. 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