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

Robustness and stability in Constraint Programming under dynamism and uncertainty

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 exist 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

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

Robustness and stability in dynamic constraint satisfaction problems

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. It is well-known that many real life problems can be modeled as Constraint Satisfaction Problems (CSPs). Much effort has been spent to increase the efficiency of algorithms for solving CSPs. However, many of these techniques assume that the set of variables, domains and constraints involved in the CSP are known and fixed when the problem is modeled. This is a strong limitation because many problems come from uncertain and dynamic environments, where both the original problem may evolve because of the environment, the user or other agents. In such situations, a solution that holds for the original problem can become invalid after changes. There are two main approaches for dealing with these situations: reactive and proactive approaches. Using reactive approaches entails re-solving the CSP after each solution loss, which is a time consuming. That is a clear disadvantage, especially when we deal with short-term changes, where solution loss is frequent. In addition, in many applications, such as on-line planning and scheduling, the delivery time of a new solution may be too long for actions to be taken on time, so a solution loss can produce several negative effects in the modeled problem. For a task assignment production system with several machines, it could cause the shutdown of the production system, the breakage of machines, the loss of the material/object in production, etc. In a transport timetabling problem, the solution loss, due to some disruption at a point, may produce a delay that propagates through the entire schedule. In addition, all the negative effects stated above will probably entail an economic loss. In this thesis we develop several proactive approaches. Proactive approaches use knowledge about possible future changes in order to avoid or minimize their effects. These approaches are applied before the changes occur. Thus, our approaches search for robust solutions, which have a high probability to remain valid after changes. Furthermore, some of our approaches also consider that the solutions can be easily adapted when they did not resist the changes in the original problem. Thus, these approaches search for stable solutions, which have an alternative solution that is similar to the previous one and therefore can be used in case of a value breakage. In this context, sometimes there exists knowledge about the uncertain and dynamic environment. However in many cases, this information is unknown or hard to obtain. For this reason, for the majority of our approaches (specifically 3 of the 4 developed approaches), the only assumptions made about changes are those inherent in the structure of problems with ordered domains. Given this framework and therefore the existence of a significant order over domain values, it is reasonable to assume that the original bounds of the solution space may undergo restrictive or relaxed modifications. Note that the possibility of solution loss only exists when changes over the original bounds of the solution space are restrictive. Therefore, the main objective for searching robust solutions in this framework is to find solutions located as far away as possible from the bounds of the solution space. In order to meet this criterion, we propose several approaches that can be divided in enumeration-based techniques and a search algorithm.Climent Aunés, LI. (2013). Robustness and stability in dynamic constraint satisfaction problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34785TESI

Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. Many real life problems come from uncertain and dynamic environments, where the initial constraints and domains may change during its execution. Thus, the solution found for the problem may become invalid. The search forrobustsolutions for constraint satisfaction problems (CSPs) has become an important issue in the ¿eld of constraint programming. In some cases, there exists knowledge about the uncertain and dynamic environment. In other cases, this information is unknown or hard to obtain. In this paper, we consider CSPs with discrete and ordered domains where changes only involve restrictions or expansions of domains or constraints. To this end, we model CSPs as weighted CSPs (WCSPs) by assigning weights to each valid tuple of the problem constraints and domains. The weight of each valid tuple is based on its distance from the borders of the space of valid tuples in the corresponding constraint/domain. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a most robust solution for the original CSP according to these assumptionsThis work has been partially supported by the research projects TIN2010-20976-C02-01 (Min. de Ciencia e Innovacion, Spain) and P19/08 (Min. de Fomento, Spain-FEDER), and the fellowship program FPU.Climent Aunés, LI.; Wallace, RJ.; Salido Gregorio, MA.; Barber Sanchís, F. (2013). Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings. Artificial Intelligence Review. 1-26. https://doi.org/10.1007/s10462-013-9420-0S126Climent L, Salido M, Barber F (2011) Reformulating dynamic linear constraint satisfaction problems as weighted csps for searching robust solutions. 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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

Master production schedule using robust optimization approaches in an automobile second-tier supplier

[EN] This paper considers a real-world automobile second-tier supplier that manufactures decorative surface finishings of injected parts provided by several suppliers, and which devises its master production schedule by a manual spreadsheet-based procedure. The imprecise production time in this manufacturer's production process is incorporated into a deterministic mathematical programming model to address this problem by two robust optimization approaches. The proposed model and the corresponding robust solution methodology improve production plans by optimizing the production, inventory and backlogging costs, and demonstrate the their feasibility for a realistic master production schedule problem that outperforms the heuristic decision-making procedure currently being applied in the firm under study.Funding was provided by Horizon 2020 Framework Programme (Grant Agreement No. 636909) in the frame of the "Cloud Collaborative Manufacturing Networks" (C2NET) project.Martín, AG.; Díaz-Madroñero Boluda, FM.; Mula, J. (2020). Master production schedule using robust optimization approaches in an automobile second-tier supplier. Central European Journal of Operations Research. 28(1):143-166. https://doi.org/10.1007/s10100-019-00607-2S143166281Alem DJ, Morabito R (2012) Production planning in furniture settings via robust optimization. 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Math Oper Res 23:769–805. https://doi.org/10.1287/moor.23.4.769Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424. https://doi.org/10.1007/PL00011380Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53. https://doi.org/10.1287/opre.1030.0065Caulkins JJ, Morrison E, Weidemann T (2007) Spreadsheet errors and decision making: evidence from field interviews. J Organ End User Comput 19:1–23Childerhouse P, Towill DR (2002) Analysis of the factors affecting real-world value stream performance. Int J Prod Res 40:3499–3518. https://doi.org/10.1080/00207540210152885Chu SCK (1995) A mathematical programming approach towards optimized master production scheduling. Int J Prod Econ 38:269–279. https://doi.org/10.1016/0925-5273(95)00015-GConlon JR (1976) Is your master production schedule feasible? Prod Invent Manag 17:56–63De La Vega J, Munari P, Morabito R (2017) Robust optimization for the vehicle routing problem with multiple deliverymen. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0511-xDíaz-Madroñero M, Mula J, Jiménez M (2014a) Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. Int J Prod Res 52:6971–6988. https://doi.org/10.1080/00207543.2014.920115Díaz-Madroñero M, Mula J, Peidro D (2014b) A review of discrete-time optimization models for tactical production planning. Int J Prod Res 52:5171–5205. https://doi.org/10.1080/00207543.2014.899721Díaz-Madroñero M, Peidro D, Mula J (2014c) A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain. Appl Math Model 38:5705–5725. https://doi.org/10.1016/j.apm.2014.04.053Dolgui A, Ben Ammar O, Hnaien F et al (2013) Supply planning and inventory control under lead time uncertainty: a review. Stud Inform Control 22:255–268Dzuranin AC, Slater RD (2014) Business risks all identified? If you’re using a spreadsheet, think again. J Corp Account Finance 25:25–30. https://doi.org/10.1002/jcaf.21936Englberger J, Herrmann F, Manitz M (2016) Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment. Int J Prod Res 54:6192–6215. https://doi.org/10.1080/00207543.2016.1162917Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: an overview. Eur J Oper Res 235:471–483Gharakhani M, Taghipour T, Farahani KJ (2010) A robust multi-objective production planning. Int J Ind Eng Comput 1:73–78. https://doi.org/10.5267/j.ijiec.2010.01.007González JJ, Reeves GR (1983) Master production scheduling: a multiple-objective linear programming approach. Int J Prod Res 21:553–562. https://doi.org/10.1080/00207548308942390Gorissen BL, Yanıkoğlu İ, den Hertog D (2015) A practical guide to robust optimization. Omega 53:124–137. https://doi.org/10.1016/j.omega.2014.12.006Grubbstrom RW, Tang O (2000) An overview of input-output analysis applied to production-inventory systems. Econ Syst Res 12:3–25. https://doi.org/10.1080/095353100111254Grubbström RW, Bogataj M, Bogataj L (2010) Optimal lotsizing within MRP theory. Annu Rev Control 34:89–100. https://doi.org/10.1016/J.ARCONTROL.2010.02.004Haojie Y, Lixin M, Canrong Z (2017) Capacitated lot-sizing problem with one-way substitution: a robust optimization approach. In: In 2017 3rd international conference on information management (ICIM). Institute of Electrical and Electronics Engineers Inc., pp 159–163Kara G, Özmen A, Weber G-W (2017) Stability advances in robust portfolio optimization under parallelepiped uncertainty. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0508-5Kawas B, Laumanns M, Pratsini E (2013) A robust optimization approach to enhancing reliability in production planning under non-compliance risks. 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Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems