On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

The relevance of outsourcing and leagile strategies in performance optimization of an integrated process planning and scheduling

Over the past few years growing global competition has forced the manufacturing industries to upgrade their old production strategies with the modern day approaches. As a result, recent interest has been developed towards finding an appropriate policy that could enable them to compete with others, and facilitate them to emerge as a market winner. Keeping in mind the abovementioned facts, in this paper the authors have proposed an integrated process planning and scheduling model inheriting the salient features of outsourcing, and leagile principles to compete in the existing market scenario. The paper also proposes a model based on leagile principles, where the integrated planning management has been practiced. In the present work a scheduling problem has been considered and overall minimization of makespan has been aimed. The paper shows the relevance of both the strategies in performance enhancement of the industries, in terms of their reduced makespan. The authors have also proposed a new hybrid Enhanced Swift Converging Simulated Annealing (ESCSA) algorithm, to solve the complex real-time scheduling problems. The proposed algorithm inherits the prominent features of the Genetic Algorithm (GA), Simulated Annealing (SA), and the Fuzzy Logic Controller (FLC). The ESCSA algorithm reduces the makespan significantly in less computational time and number of iterations. The efficacy of the proposed algorithm has been shown by comparing the results with GA, SA, Tabu, and hybrid Tabu-SA optimization methods

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

BASA: An improved hybrid bees algorithm for the single machine scheduling with early/tardy jobs

[EN] In this paper, we present a novel hybrid meta-heuristic by enhancing the Basic Bees Algorithm through the integration of a local search method namely Simulated Annealing and Variable Neighbourhood Search like algorithm. The resulted hybrid bees algorithm (BASA) is used to solve the Single Machine Scheduling Problem with Early/Tardy jobs, where the generated outcomes are compared against the Basic Bees Algorithm (BA), and against some stat-of-the-art meta-heuristics. Computational results reveal that our proposed framework outperforms the Basic Bees Algorithm, and demonstrates a competitive performance compared with some algorithms extracted from the literature.Abdessemed, AA.; Mouss, LH.; Benaggoune, K. (2023). BASA: An improved hybrid bees algorithm for the single machine scheduling with early/tardy jobs. International Journal of Production Management and Engineering. 11(2):167-177. https://doi.org/10.4995/ijpme.2023.18077167177112Abdul-Razaq, T. S., & Potts, C. N. (1988). 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In Mexican International Conference on Artificial Intelligence (pp. 664-674). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_63Lim, C. H., Lim, S., How, B. S., Ng, W. P. Q., Ngan, S. L., Leong, W. D., & Lam, H. L. (2021). A review of industry 4.0 revolution potential in a sustainable and renewable palm oil industry: HAZOP approach. Renewable and Sustainable Energy Reviews, 135, 110223. https://doi.org/10.33932/rir.44.3.2Mei, C. A., Pham, D. T., Anthony, J. S., & Kok, W. N. (2010, November). PCB assembly optimisation using the Bees Algorithm enhanced with TRIZ operators. In IECON 2010-36th Annual Conference on IEEE Industrial Electronics Society (pp. 2708-2713). IEEE. https://doi.org/10.1109/IECON.2010.5675114M'Hallah, R., & Alhajraf, A. (2016). Ant colony systems for the single-machine total weighted earliness tardiness scheduling problem. Journal of Scheduling, 19(2), 191-205. https://doi.org/10.1007/s10951-015-0429-xNguyen, K., Nguyen, P., & Tran, N. (2012). A hybrid algorithm of harmony search and bees algorithm for a university course timetabling problem. International Journal of Computer Science Issues (IJCSI), 9(1), 12.Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., & Zaidi, M. (2006). The bees algorithm-a novel tool for complex optimisation problems. In Intelligent production machines and systems (pp. 454-459). Elsevier Science Ltd. https://doi.org/10.1177/0959651811422759Pham, D. T., Koc, E., Lee, J. Y., & Phrueksanant, J. (2007a). Using the bees algorithm to schedule jobs for a machine. In Proceedings Eighth International Conference on Laser Metrology, CMM and Machine Tool Performance, LAMDAMAP, Euspen, UK, Cardiff (pp. 430-439).Pham, D. T., Otri, S., & Darwish, A. H. (2007b). Application of the Bees Algorithm to PCB assembly optimisation. In Proceedings of the 3rd virtual international conference on intelligent production machines and systems (IPROMS 2007) (pp. 511-516).Pham, D. T., Castellani, M., & Fahmy, A. A. (2008). Learning the inverse kinematics of a robot manipulator using the bees algorithm. In 2008 6th IEEE International Conference on Industrial Informatics (pp. 493-498). IEEE. https://doi.org/10.1109/INDIN.2008.4618151Pham, Q. T., Pham, D. T., & Castellani, M. (2012). A modified bees algorithm and a statistics-based method for tuning its parameters. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(3), 287-301. https://doi.org/10.1177/0959651811422759Seeley, T. D. (2009). The wisdom of the hive: the social physiology of honey bee colonies. Harvard University Press. https://doi.org/10.2307/j.ctv1kz4h15Sourd, F. (2009). New exact algorithms for one-machine earliness-tardiness scheduling. INFORMS Journal on Computing, 21(1), 167-175. https://doi.org/10.1287/ijoc.1080.0287Sourd, F., & Kedad-Sidhoum, S. (2008). A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem. 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The automatic design of hyper-heuristic framework with gene expression programming for combinatorial optimization problems

Hyper-heuristic approaches aim to automate heuristic design in order to solve multiple problems instead of designing tailor-made methodologies for individual problems. Hyper-heuristics accomplish this through a high level heuristic (heuristic selection mechanism and an acceptance criterion). This automates heuristic selection, deciding whether to accept or reject the returned solution. The fact that different problems or even instances, have different landscape structures and complexity, the design of efficient high level heuristics can have a dramatic impact on hyper-heuristic performance. In this work, instead of using human knowledge to design the high level heuristic, we propose a gene expression programming algorithm to automatically generate, during the instance solving process, the high level heuristic of the hyper-heuristic framework. The generated heuristic takes information (such as the quality of the generated solution and the improvement made) from the current problem state as input and decides which low level heuristic should be selected and the acceptance or rejection of the resultant solution. The benefit of this framework is the ability to generate, for each instance, different high level heuristics during the problem solving process. Furthermore, in order to maintain solution diversity, we utilize a memory mechanism which contains a population of both high quality and diverse solutions that is updated during the problem solving process. The generality of the proposed hyper-heuristic is validated against six well known combinatorial optimization problem, with very different landscapes, provided by the HyFlex software. Empirical results comparing the proposed hyper-heuristic with state of the art hyper-heuristics, conclude that the proposed hyper-heuristic generalizes well across all domains and achieves competitive, if not superior, results for several instances on all domains

Grammatical evolution hyper-heuristic for combinatorial optimization problems

Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves templates of perturbation heuristics. The evolved templates are improvement heuristics, which represent a complete search method to solve the problem at hand. To test the generality and the performance of the proposed method, we consider two well-known combinatorial optimization problems: exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden instances). We demonstrate that the proposed method is competitive, if not superior, when compared to state-of-the-art hyper-heuristics, as well as bespoke methods for these different problem domains. In order to further improve the performance of the proposed framework we utilize an adaptive memory mechanism, which contains a collection of both high quality and diverse solutions and is updated during the problem solving process. Experimental results show that the grammatical evolution hyper-heuristic, with an adaptive memory, performs better than the grammatical evolution hyper-heuristic without a memory. The improved framework also outperforms some bespoke methodologies, which have reported best known results for some instances in both problem domains

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Variable Annealing Length and Parallelism in Simulated Annealing

In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing schedule, which adaptively controls the temperature parameter to track a theoretically ideal rate of acceptance of neighboring states. A sequential implementation of Modified Lam simulated annealing is almost parameter-free. However, it requires prior knowledge of the annealing length. We eliminate this parameter using restarts, with an exponentially increasing schedule of annealing lengths. We then extend this restart schedule to parallel implementation, executing several Modified Lam simulated annealers in parallel, with varying initial annealing lengths, and our proposed parallel annealing length schedule. To validate our approach, we conduct experiments on an NP-Hard scheduling problem with sequence-dependent setup constraints. We compare our approach to fixed length restarts, both sequentially and in parallel. Our results show that our approach can achieve substantial performance gains, throughout the course of the run, demonstrating our approach to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10. June 201