Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Hybrid metaheuristics for the accessibility windows assembly line balancing problem level 2 (AWALBP-L2)

This paper addresses an assembly line balancing problem in which the length of the workpieces is larger than the width of the workstations. The problem differs from traditional variants of assembly line balancing in the sense that only a portion of the workpiece, or portions of two consecutive workpieces, can be reached from any workstation. Consequently, at any stationary stage of the cycle, each workstation can only process a portion of the tasks, namely, those which are inside the area of a workpiece that is reachable from the workstation. The objective is to find a (cyclic) movement scheme of the workpieces along the line and a task assignment to stationary stages of the production process, while minimizing the cycle time. We propose three hybrid approaches of metaheuristics and mathematical programming - one based on simulated annealing and the other two based on tabu search, relying on different neighborhood definitions. The two former approaches make use of a classical neighborhood, obtained by applying local changes to a current solution. The latter approach, in contrast, draws ideas from the corridor method to define a corridor around the current solution, via the imposition of exogenous constraints on the solution space of the problem. An extensive computational experiment is carried out to test the performance of the proposed approaches, improving the best results published to date.Postprint (author's final draft

Solving the bi-objective capacitated p -median problem with multilevel capacities using compromise programming and VNS

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.A bi‐objective optimisation using a compromise programming (CP) approach is proposed for the capacitated p‐median problem (CPMP) in the presence of the fixed cost of opening facility and several possible capacities that can be used by potential facilities. As the sum of distances between customers and their facilities and the total fixed cost for opening facilities are important aspects, the model is proposed to deal with those conflicting objectives. We develop a mathematical model using integer linear programming (ILP) to determine the optimal location of open facilities with their optimal capacity. Two approaches are designed to deal with the bi‐objective CPMP, namely CP with an exact method and with a variable neighbourhood search (VNS) based matheuristic. New sets of generated instances are used to evaluate the performance of the proposed approaches. The computational experiments show that the proposed approaches produce interesting results

A survey on financial applications of metaheuristics

Modern heuristics or metaheuristics are optimization algorithms that have been increasingly used during the last decades to support complex decision-making in a number of fields, such as logistics and transportation, telecommunication networks, bioinformatics, finance, and the like. The continuous increase in computing power, together with advancements in metaheuristics frameworks and parallelization strategies, are empowering these types of algorithms as one of the best alternatives to solve rich and real-life combinatorial optimization problems that arise in a number of financial and banking activities. This article reviews some of the works related to the use of metaheuristics in solving both classical and emergent problems in the finance arena. A non-exhaustive list of examples includes rich portfolio optimization, index tracking, enhanced indexation, credit risk, stock investments, financial project scheduling, option pricing, feature selection, bankruptcy and financial distress prediction, and credit risk assessment. This article also discusses some open opportunities for researchers in the field, and forecast the evolution of metaheuristics to include real-life uncertainty conditions into the optimization problems being considered.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P, TRA2015-71883-REDT), FEDER, and the Universitat Jaume I mobility program (E-2015-36)

AWALBP-L2 : the Accessibility Windows Assembly Line Balancing Problem Level 2 : formalization and solution methods

This doctoral thesis tackles an assembly line balancing problem with restricted access to the workpieces that has been entitled AWALBP: the Accessibility Windows Assembly Line Balancing Problem. The problem is described and a general classification for its main optimization levels is proposed. The thesis focuses on a specific case of the optimization level AWALBP-L2. The AWALBP-L2 consists of two subproblems that need to be solved simultaneously: (i) the computation of a feasible movement scheme and (ii) the assignment of each task to one workstation and one stationary stage of the cycle. In the particular case of AWALBP-L2 addressed in this thesis, for each task a single workstation is compatible. The review of the state of the art reveals that relatively few studies have been published concerning the AWALBP. Regarding the solution of the AWALBP-L2, the only available previous work is a mathematical programming model, but the model is not tested or validated. In order to fill this research gap, the aim of this thesis is three-fold: i) to describe the AWALBP and characterize its main optimization levels, ii) to propose exact methods for the case of AWALBP-L2 considered, and iii) to develop solution procedures for the challenging instances that are out of reach of the former methods. Consequently, in this doctoral thesis the AWALBP is characterized and the AWALBP-L2 case is addressed through four main approaches. First, the problem is formalized and solved via two mixed integer linear programming (MILP) models. Second, an approach combining a matheuristic and a MILP model is proposed. The third approach considers hybridizing metaheuristics with mathematical programming models. Finally, the fourth approach proposes sequential combinations of the aforementioned hybrid metaheuristics and a MILP model. The performance of all approaches is evaluated via an extensive computational experiment based on realistic instances, and an optimal solution could be found for a large number of them. Future research work may include additional assumptions on the problem, such as precedence relationships among tasks or several workstations compatible for each task. The methods proposed in this thesis are open in nature and extend perspectives for combining (meta)heuristics and mathematical programming models, either for improving the solution of the AWALBP-L2 or for tackling other combinatorial optimization problems.Esta tesis doctoral aborda un problema de equilibrado de líneas con acceso limitado a las piezas que ha sido titulado AWALBP: Accessibility Windows Assembly Line Balancing Problem. Se describe el problema y se propone una clasificación general de sus principales niveles de optimización. La tesis se centra en un caso específico del nivel AWALBP-L2. El AWALBP-L2 consta de dos subproblemas que deben ser resueltos simultáneamente: (i) cálculo de un esquema de movimiento factible y (ii) asignación de cada tarea a una estación y a una de las etapas estacionarias del ciclo. En el caso particular de AWALBP-L2 tratado en esta tesis, para cada tarea existe una única estación compatible. La revisión del estado del arte revela que relativamente pocos estudios han sido publicados sobre el AWALBP. Respecto a la resolución del AWALBP-L2, el único trabajo anterior disponible es un modelo de programación matemática, el cual no está probado o validado. Con tal de cubrir este hueco de investigación, el objetivo de la presente tesis es triple: i) describir el AWALBP y caracterizar sus principales niveles de optimización, ii) proponer métodos exactos para el caso considerado de AWALBP-L2, y iii) desarrollar métodos de resolución para los ejemplares más difíciles que quedaron fuera del alcance de los métodos anteriores. Por consiguiente, en esta tesis doctoral se caracteriza el AWALBP y se aborda el caso de AWALBP-L2 mediante cuatro enfoques principales. En primer lugar, el problema se formaliza y se resuelve mediante dos modelos de programación lineal entera mixta (PLEM). En segundo lugar se propone una mateheurística combinada con un modelo de PLEM. El tercer enfoque consiste en hibridizar metaheurísticas con modelos de programación matemática. Finalmente, el cuarto enfoque propone combinaciones secuenciales de las mencionadas metaheurísticas híbridas con un modelo de PLEM. Los enfoques propuestos se evalúan mediante una extensa experiencia computacional con ejemplares realistas, y se obtuvo una solución óptima para un gran número de ellos. Las líneas propuestas de investigación futura incluyen supuestos adicionales tales como relaciones de precedencia entre tareas o varias estaciones compatibles para una misma tarea. Los métodos propuestos en esta tesis son de naturaleza abierta y ofrecen perspectivas para la combinación de (meta)heurísticas con modelos de programación matemática, tanto para mejorar la solución del AWALBP-L2 como para abordar otros problemas de optimización combinatoria

A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem

[EN] The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental impact. From the point of view of computational complexity, the problem is challenging due to the large number of possible combinations in the solution space. In this article, a k-means cuckoo search hybrid algorithm is proposed where the cuckoo search metaheuristic is used as an optimization mechanism in continuous spaces and the unsupervised k-means learning technique to discretize the solutions. A random operator is designed to determine the contribution of the k-means operator in the optimization process. The best values, the averages, and the interquartile ranges of the obtained distributions are compared. The hybrid algorithm was later compared to a version of harmony search that also solved the problem. The results show that the k-mean operator contributes significantly to the quality of the solutions and that our algorithm is highly competitive, surpassing the results obtained by harmony search.The first author was supported by the Grant CONICYT/FONDECYT/INICIACION/11180056, the other two authors were supported by the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).García, J.; Yepes, V.; Martí Albiñana, JV. (2020). A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem. Mathematics. 8(4):1-22. https://doi.org/10.3390/math8040555S12284García, J., Altimiras, F., Peña, A., Astorga, G., & Peredo, O. (2018). A Binary Cuckoo Search Big Data Algorithm Applied to Large-Scale Crew Scheduling Problems. Complexity, 2018, 1-15. doi:10.1155/2018/8395193García, J., Moraga, P., Valenzuela, M., Crawford, B., Soto, R., Pinto, H., … Astorga, G. (2019). A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems. Computational Intelligence and Neuroscience, 2019, 1-16. doi:10.1155/2019/3238574Al-Madi, N., Faris, H., & Mirjalili, S. (2019). Binary multi-verse optimization algorithm for global optimization and discrete problems. International Journal of Machine Learning and Cybernetics, 10(12), 3445-3465. doi:10.1007/s13042-019-00931-8Kim, M., & Chae, J. (2019). Monarch Butterfly Optimization for Facility Layout Design Based on a Single Loop Material Handling Path. Mathematics, 7(2), 154. doi:10.3390/math7020154García, J., Crawford, B., Soto, R., & Astorga, G. (2019). A clustering algorithm applied to the binarization of Swarm intelligence continuous metaheuristics. Swarm and Evolutionary Computation, 44, 646-664. doi:10.1016/j.swevo.2018.08.006García, J., Lalla-Ruiz, E., Voß, S., & Droguett, E. L. (2020). Enhancing a machine learning binarization framework by perturbation operators: analysis on the multidimensional knapsack problem. International Journal of Machine Learning and Cybernetics, 11(9), 1951-1970. doi:10.1007/s13042-020-01085-8García, J., Moraga, P., Valenzuela, M., & Pinto, H. (2020). A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem. Mathematics, 8(4), 507. doi:10.3390/math8040507Saeheaw, T., & Charoenchai, N. (2018). A comparative study among different parallel hybrid artificial intelligent approaches to solve the capacitated vehicle routing problem. International Journal of Bio-Inspired Computation, 11(3), 171. doi:10.1504/ijbic.2018.091704Valdez, F., Castillo, O., Jain, A., & Jana, D. K. (2019). Nature-Inspired Optimization Algorithms for Neuro-Fuzzy Models in Real-World Control and Robotics Applications. Computational Intelligence and Neuroscience, 2019, 1-2. doi:10.1155/2019/9128451Penadés-Plà, V., García-Segura, T., & Yepes, V. (2020). Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge. Mathematics, 8(3), 398. doi:10.3390/math8030398García-Segura, T., Yepes, V., Frangopol, D. M., & Yang, D. Y. (2017). Lifetime reliability-based optimization of post-tensioned box-girder bridges. Engineering Structures, 145, 381-391. doi:10.1016/j.engstruct.2017.05.013Yepes, V., Martí, J. V., & García, J. (2020). Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls. Sustainability, 12(7), 2767. doi:10.3390/su12072767Marti-Vargas, J. R., Ferri, F. J., & Yepes, V. (2013). Prediction of the transfer length of prestressing strands with neural networks. Computers and Concrete, 12(2), 187-209. doi:10.12989/cac.2013.12.2.187Fu, W., Tan, J., Zhang, X., Chen, T., & Wang, K. (2019). Blind Parameter Identification of MAR Model and Mutation Hybrid GWO-SCA Optimized SVM for Fault Diagnosis of Rotating Machinery. Complexity, 2019, 1-17. doi:10.1155/2019/3264969Sierra, L. A., Yepes, V., García-Segura, T., & Pellicer, E. (2018). Bayesian network method for decision-making about the social sustainability of infrastructure projects. Journal of Cleaner Production, 176, 521-534. doi:10.1016/j.jclepro.2017.12.140Crawford, B., Soto, R., Astorga, G., García, J., Castro, C., & Paredes, F. (2017). Putting Continuous Metaheuristics to Work in Binary Search Spaces. Complexity, 2017, 1-19. doi:10.1155/2017/8404231Hatamlou, A. (2013). Black hole: A new heuristic optimization approach for data clustering. Information Sciences, 222, 175-184. doi:10.1016/j.ins.2012.08.023Pan, W.-T. (2012). A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example. Knowledge-Based Systems, 26, 69-74. doi:10.1016/j.knosys.2011.07.001Rashedi, E., Nezamabadi-pour, H., & Saryazdi, S. (2009). GSA: A Gravitational Search Algorithm. Information Sciences, 179(13), 2232-2248. doi:10.1016/j.ins.2009.03.004Calvet, L., Armas, J. de, Masip, D., & Juan, A. A. (2017). Learnheuristics: hybridizing metaheuristics with machine learning for optimization with dynamic inputs. Open Mathematics, 15(1), 261-280. doi:10.1515/math-2017-0029Talbi, E.-G. (2015). Combining metaheuristics with mathematical programming, constraint programming and machine learning. Annals of Operations Research, 240(1), 171-215. doi:10.1007/s10479-015-2034-yJuan, A. A., Faulin, J., Grasman, S. E., Rabe, M., & Figueira, G. (2015). A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems. Operations Research Perspectives, 2, 62-72. doi:10.1016/j.orp.2015.03.001Chou, J.-S., & Nguyen, T.-K. (2018). Forward Forecast of Stock Price Using Sliding-Window Metaheuristic-Optimized Machine-Learning Regression. IEEE Transactions on Industrial Informatics, 14(7), 3132-3142. doi:10.1109/tii.2018.2794389Sayed, G. I., Tharwat, A., & Hassanien, A. E. (2018). Chaotic dragonfly algorithm: an improved metaheuristic algorithm for feature selection. Applied Intelligence, 49(1), 188-205. doi:10.1007/s10489-018-1261-8De León, A. D., Lalla-Ruiz, E., Melián-Batista, B., & Marcos Moreno-Vega, J. (2017). A Machine Learning-based system for berth scheduling at bulk terminals. Expert Systems with Applications, 87, 170-182. doi:10.1016/j.eswa.2017.06.010García, J., Crawford, B., Soto, R., Castro, C., & Paredes, F. (2017). A k-means binarization framework applied to multidimensional knapsack problem. Applied Intelligence, 48(2), 357-380. doi:10.1007/s10489-017-0972-6Molina-Moreno, F., Martí, J. V., & Yepes, V. (2017). Carbon embodied optimization for buttressed earth-retaining walls: Implications for low-carbon conceptual designs. Journal of Cleaner Production, 164, 872-884. doi:10.1016/j.jclepro.2017.06.246Asta, S., Özcan, E., & Curtois, T. (2016). A tensor based hyper-heuristic for nurse rostering. Knowledge-Based Systems, 98, 185-199. doi:10.1016/j.knosys.2016.01.031Martin, S., Ouelhadj, D., Beullens, P., Ozcan, E., Juan, A. A., & Burke, E. K. (2016). A multi-agent based cooperative approach to scheduling and routing. European Journal of Operational Research, 254(1), 169-178. doi:10.1016/j.ejor.2016.02.045Ghazali, R., Deris, M. M., Nawi, N. M., & Abawajy, J. H. (Eds.). (2018). Recent Advances on Soft Computing and Data Mining. Advances in Intelligent Systems and Computing. doi:10.1007/978-3-319-72550-5Veček, N., Mernik, M., Filipič, B., & Črepinšek, M. (2016). Parameter tuning with Chess Rating System (CRS-Tuning) for meta-heuristic algorithms. Information Sciences, 372, 446-469. doi:10.1016/j.ins.2016.08.066Ries, J., & Beullens, P. (2015). A semi-automated design of instance-based fuzzy parameter tuning for metaheuristics based on decision tree induction. Journal of the Operational Research Society, 66(5), 782-793. doi:10.1057/jors.2014.46Yalcinoz, T., & Altun, H. (2001). Power economic dispatch using a hybrid genetic algorithm. IEEE Power Engineering Review, 21(3), 59-60. doi:10.1109/39.911360Kaur, H., Virmani, J., Kriti, & Thakur, S. (2019). A genetic algorithm-based metaheuristic approach to customize a computer-aided classification system for enhanced screen film mammograms. U-Healthcare Monitoring Systems, 217-259. doi:10.1016/b978-0-12-815370-3.00010-4Faris, H., Hassonah, M. A., Al-Zoubi, A. M., Mirjalili, S., & Aljarah, I. (2017). A multi-verse optimizer approach for feature selection and optimizing SVM parameters based on a robust system architecture. Neural Computing and Applications, 30(8), 2355-2369. doi:10.1007/s00521-016-2818-2Faris, H., Aljarah, I., & Mirjalili, S. (2017). Improved monarch butterfly optimization for unconstrained global search and neural network training. Applied Intelligence, 48(2), 445-464. doi:10.1007/s10489-017-0967-3Chou, J.-S., & Thedja, J. P. P. (2016). Metaheuristic optimization within machine learning-based classification system for early warnings related to geotechnical problems. Automation in Construction, 68, 65-80. doi:10.1016/j.autcon.2016.03.015Pham, A.-D., Hoang, N.-D., & Nguyen, Q.-T. (2016). Predicting Compressive Strength of High-Performance Concrete Using Metaheuristic-Optimized Least Squares Support Vector Regression. Journal of Computing in Civil Engineering, 30(3), 06015002. doi:10.1061/(asce)cp.1943-5487.0000506Göçken, M., Özçalıcı, M., Boru, A., & Dosdoğru, A. T. (2016). Integrating metaheuristics and Artificial Neural Networks for improved stock price prediction. Expert Systems with Applications, 44, 320-331. doi:10.1016/j.eswa.2015.09.029Chou, J.-S., & Pham, A.-D. (2017). Nature-inspired metaheuristic optimization in least squares support vector regression for obtaining bridge scour information. Information Sciences, 399, 64-80. doi:10.1016/j.ins.2017.02.051Kuo, R. J., Lin, T. C., Zulvia, F. E., & Tsai, C. Y. (2018). A hybrid metaheuristic and kernel intuitionistic fuzzy c-means algorithm for cluster analysis. Applied Soft Computing, 67, 299-308. doi:10.1016/j.asoc.2018.02.039Singh Mann, P., & Singh, S. (2017). Energy efficient clustering protocol based on improved metaheuristic in wireless sensor networks. Journal of Network and Computer Applications, 83, 40-52. doi:10.1016/j.jnca.2017.01.031Rosa, R. de A., Machado, A. M., Ribeiro, G. M., & Mauri, G. R. (2016). A mathematical model and a Clustering Search metaheuristic for planning the helicopter transportation of employees to the production platforms of oil and gas. Computers & Industrial Engineering, 101, 303-312. doi:10.1016/j.cie.2016.09.006Faris, H., Mirjalili, S., & Aljarah, I. (2019). Automatic selection of hidden neurons and weights in neural networks using grey wolf optimizer based on a hybrid encoding scheme. International Journal of Machine Learning and Cybernetics, 10(10), 2901-2920. doi:10.1007/s13042-018-00913-2De Rosa, G. H., Papa, J. P., & Yang, X.-S. (2017). Handling dropout probability estimation in convolution neural networks using meta-heuristics. Soft Computing, 22(18), 6147-6156. doi:10.1007/s00500-017-2678-4Rere, L. M. R., Fanany, M. I., & Arymurthy, A. M. (2016). Metaheuristic Algorithms for Convolution Neural Network. Computational Intelligence and Neuroscience, 2016, 1-13. doi:10.1155/2016/1537325Jothi, R., Mohanty, S. K., & Ojha, A. (2017). DK-means: a deterministic K-means clustering algorithm for gene expression analysis. Pattern Analysis and Applications, 22(2), 649-667. doi:10.1007/s10044-017-0673-0García, J., Pope, C., & Altimiras, F. (2017). A Distributed K-Means Segmentation Algorithm Applied to Lobesia botrana Recognition. Complexity, 2017, 1-14. doi:10.1155/2017/5137317Arunkumar, N., Mohammed, M. A., Abd Ghani, M. K., Ibrahim, D. A., Abdulhay, E., Ramirez-Gonzalez, G., & de Albuquerque, V. H. C. (2018). K-Means clustering and neural network for object detecting and identifying abnormality of brain tumor. Soft Computing, 23(19), 9083-9096. doi:10.1007/s00500-018-3618-7Abdel-Basset, M., Wang, G.-G., Sangaiah, A. K., & Rushdy, E. (2017). Krill herd algorithm based on cuckoo search for solving engineering optimization problems. Multimedia Tools and Applications, 78(4), 3861-3884. doi:10.1007/s11042-017-4803-xChi, R., Su, Y., Zhang, D., Chi, X., & Zhang, H. (2017). A hybridization of cuckoo search and particle swarm optimization for solving optimization problems. Neural Computing and Applications, 31(S1), 653-670. doi:10.1007/s00521-017-3012-xLi, J., Xiao, D., Lei, H., Zhang, T., & Tian, T. (2020). Using Cuckoo Search Algorithm with Q-Learning and Genetic Operation to Solve the Problem of Logistics Distribution Center Location. Mathematics, 8(2), 149. doi:10.3390/math8020149Pan, J.-S., Song, P.-C., Chu, S.-C., & Peng, Y.-J. (2020). Improved Compact Cuckoo Search Algorithm Applied to Location of Drone Logistics Hub. Mathematics, 8(3), 333. doi:10.3390/math8030333Yepes, V., Alcala, J., Perea, C., & González-Vidosa, F. (2008). A parametric study of optimum earth-retaining walls by simulated annealing. Engineering Structures, 30(3), 821-830. doi:10.1016/j.engstruct.2007.05.023Molina-Moreno, F., García-Segura, T., Martí, J. V., & Yepes, V. (2017). Optimization of buttressed earth-retaining walls using hybrid harmony search algorithms. Engineering Structures, 134, 205-216. doi:10.1016/j.engstruct.2016.12.04