Justin Pauckert
ABSTRACT
Quadratic Unconstrained Binary Optimization (QUBO) has emerged as a vital unifying model for combinatorial optimization problems, and (meta-)heuristic approaches are commonly used to solve them due to their NP-hard nature. Scatter Search (SS), a population-based metaheuristic framework, is one such method that has shown promising results for QUBO problems. Generating new solutions from more promising ones is a crucial operation in SS. Path Relinking (PR) based SS has been previously used to solve challenging QUBO problems with high-quality solutions. This paper introduces two new variants of the SS algorithm. The first is the (Multi) Uniform Crossover (MUC) based SS while the second is the Univariate Marginal Distribution Algorithm (UMDA) based SS. MUC and UMDA are well-known operators in Genetic Algorithms and Estimation of Distribution Algorithms respectively. When compared to the existing PR based SS, this work shows that more promising results can be achieved when the newly proposed MUC and UMDA-based SS are applied to QUBO formulations of the Quadratic Knapsack Problem (QKP) instances.
- Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. 2019. Optuna: A Next-Generation Hyperparameter Optimization Framework. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (Anchorage, AK, USA) (KDD '19). Association for Computing Machinery, New York, NY, USA, 2623--2631. Google Scholar
Digital Library
- Talal M Alkhamis, Merza Hasan, and Mohamed A Ahmed. 1998. Simulated annealing for the unconstrained quadratic pseudo-Boolean function. European Journal of Operational Research 108, 3 (1998), 641--652.Google ScholarCross Ref
- Mohammad M. Amini, Bahram Alidaee, and Gary A. Kochenberger. 1999. A Scatter Search Approach to Unconstrained Quadratic Binary Programs. McGraw-Hill Ltd., UK, GBR, 317--330.Google Scholar
- Maliheh Aramon, Gili Rosenberg, Elisabetta Valiante, Toshiyuki Miyazawa, Hirotaka Tamura, and Helmut G. Katzgraber. 2019. Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer. Frontiers in Physics 7 (2019), 48. Google ScholarCross Ref
- Mayowa Ayodele. 2022. Comparing the Digital Annealer with Classical Evolutionary Algorithm. Google ScholarCross Ref
- Shummet Baluja. 1994. Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Technical Report. Carnegie Mellon University, USA.Google Scholar
- Vahid Beiranvand, Warren Hare, and Yves Lucet. 2017. Best practices for comparing optimization algorithms. Optimization and Engineering 18, 4 (2017), 815--848.Google ScholarCross Ref
- James Bergstra, Brent Komer, Chris Eliasmith, Dan Yamins, and David D Cox. 2015. Hyperopt: a python library for model selection and hyperparameter optimization. Computational Science & Discovery 8, 1 (2015), 014008.Google ScholarCross Ref
- Alain Billionnet and Éric Soutif. 2004. Using a Mixed Integer Programming Tool for Solving the 0--1 Quadratic Knapsack Problem. INFORMS Journal on Computing 16, 2 (2004), 188--197. arXiv:https://doi.org/10.1287/ijoc.1030.0029 Google ScholarDigital Library
- Zhiwei Cao, Yichao Zhang, Jihong Guan, and Shuigeng Zhou. 2018. Link prediction based on quantum-inspired ant colony optimization. Scientific reports 8, 1 (2018), 1--11.Google Scholar
- Barry A Cipra. 1987. An introduction to the Ising model. The American Mathematical Monthly 94, 10 (1987), 937--959.Google ScholarDigital Library
- Wu Deng, Hailong Liu, Junjie Xu, Huimin Zhao, and Yingjie Song. 2020. An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Transactions on Instrumentation and Measurement 69, 10 (2020), 7319--7327.Google ScholarCross Ref
- Iain Dunning, Swati Gupta, and John Silberholz. 2018. What works best when? A systematic evaluation of heuristics for Max-Cut and QUBO. INFORMS Journal on Computing 30, 3 (2018), 608--624.Google ScholarDigital Library
- Katharina Eggensperger, Marius Lindauer, and Frank Hutter. 2019. Pitfalls and best practices in algorithm configuration. Journal of Artificial Intelligence Research 64 (2019), 861--893.Google ScholarDigital Library
- Noriyuki Fujimoto and Kouki Nanai. 2021. Solving QUBO with GPU Parallel MOPSO. In Proceedings of the Genetic and Evolutionary Computation Conference Companion (Lille, France) (GECCO '21). Association for Computing Machinery, New York, NY, USA, 1788--1794. Google ScholarDigital Library
- Fred Glover and Jin-Kao Hao. 2010. Efficient evaluations for solving large 0--1 unconstrained quadratic optimisation problems. International Journal of Metaheuristics 1, 1 (2010), 3--10.Google ScholarDigital Library
- Fred Glover, Gary A Kochenberger, and Bahram Alidaee. 1998. Adaptive memory tabu search for binary quadratic programs. Management Science 44, 3 (1998), 336--345.Google ScholarDigital Library
- Huseyin Hakli and Zeynep Ortacay. 2019. An improved scatter search algorithm for the uncapacitated facility location problem. Computers & Industrial Engineering 135 (2019), 855--867. Google ScholarDigital Library
- Nakayama Hiroshi, Koyama Junpei, Yoneoka Noboru, and Miyazawa Toshiyuki. 2021. Third Generation Digital Annealer Technology. https://www.fujitsu.com/jp/documents/digitalannealer/researcharticles/DA_WP_EN_20210922.pdfGoogle Scholar
- Changwu Huang, Yuanxiang Li, and Xin Yao. 2019. A survey of automatic parameter tuning methods for metaheuristics. IEEE transactions on evolutionary computation 24, 2 (2019), 201--216.Google Scholar
- Mark W Johnson, Mohammad HS Amin, Suzanne Gildert, Trevor Lanting, Firas Hamze, Neil Dickson, Richard Harris, Andrew J Berkley, Jan Johansson, Paul Bunyk, et al. 2011. Quantum annealing with manufactured spins. Nature 473, 7346 (2011), 194--198.Google Scholar
- Patrick Koch, Oleg Golovidov, Steven Gardner, Brett Wujek, Joshua Griffin, and Yan Xu. 2018. Autotune: A Derivative-Free Optimization Framework for Hyperparameter Tuning. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (London, United Kingdom) (KDD '18). Association for Computing Machinery, New York, NY, USA, 443--452. Google ScholarDigital Library
- Gary Kochenberger, Jin-Kao Hao, Fred Glover, Mark Lewis, Zhipeng Lü, Haibo Wang, and Yang Wang. 2014. The unconstrained binary quadratic programming problem: a survey. Journal of combinatorial optimization 28, 1 (2014), 58--81.Google ScholarDigital Library
- Pedro Larranaga and Jose Lozano. 2002. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Springer, Berlin, Heidelberg. Google ScholarCross Ref
- Manuel López-Ibáñez, Jérémie Dubois-Lacoste, Leslie Pérez Cáceres, Mauro Birattari, and Thomas Stützle. 2016. The irace package: Iterated racing for automatic algorithm configuration. Operations Research Perspectives 3 (2016), 43--58.Google ScholarCross Ref
- Andrew Lucas. 2014. Ising formulations of many NP problems. Frontiers in Physics 2 (2014), Article 5. Google ScholarCross Ref
- Satoshi Matsubara, Motomu Takatsu, Toshiyuki Miyazawa, Takayuki Shibasaki, Yasuhiro Watanabe, Kazuya Takemoto, and Hirotaka Tamura. 2020. Digital Annealer for High-Speed Solving of Combinatorial optimization Problems and Its Applications. In 2020 25th Asia and South Pacific Design Automation Conference (ASP-DAC). IEEE, Beijing, China, 667--672. Google ScholarDigital Library
- Peter Merz and Kengo Katayama. 2004. Memetic algorithms for the unconstrained binary quadratic programming problem. BioSystems 78, 1--3 (2004), 99--118.Google ScholarCross Ref
- Eduardo Moreno, Daniel Espinoza, and Marcos Goycoolea. 2010. Large-scale multi-period precedence constrained knapsack problem: a mining application. Electronic notes in discrete mathematics 36 (2010), 407--414.Google Scholar
- H. Mühlenbein and G. Paaß. 1996. From recombination of genes to the estimation of distributions I. Binary parameters. Lecture Notes in Computer Science 1141 (1996), 178--187.Google ScholarDigital Library
- Gita Naseri and Mattheos AG Koffas. 2020. Application of combinatorial optimization strategies in synthetic biology. Nature communications 11, 1 (2020), 1--14.Google Scholar
- Gintaras Palubeckis. 2004. Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem. Annals of Operations Research 131 (2004), 259--282.Google ScholarCross Ref
- Matthieu Parizy, Norihiro Kakuko, and Nozomu Togawa. 2023. Fast Hyperparameter Tuning for Ising Machines. In 2023 IEEE International Conference on Consumer Electronics (ICCE). 1--6. Google ScholarCross Ref
- Matthieu Parizy and Nozomu Togawa. 2021. Analysis and Acceleration of the Quadratic Knapsack Problem on an Ising Machine. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences advpub (2021), 2020KEP0007. Google ScholarCross Ref
- C. Patvardhan, Sulabh Bansal, and A. Srivastav. 2015. Solving the 0--1 Quadratic Knapsack Problem with a competitive Quantum Inspired Evolutionary Algorithm. J. Comput. Appl. Math. 285 (2015), 86--99. Google ScholarDigital Library
- Justin Pauckert, Matthieu Parizy, and Ayodele Mayowa. 2022. Strategic Solution Combination in Scatter Search for Quadratic Unconstrained Binary Optimization. In Proceedings of The 14th International Conference on Evolutionary Computation Theory and Applications (ECTA). SCITEPRESS, 133--142. https://www.scitepress.org/Papers/2022/115476/115476.pdfGoogle ScholarCross Ref
- Stjepan Picek, Marin Golub, and Domagoj Jakobovic. 2011. Evaluation of Crossover Operator Performance in Genetic Algorithms with Binary Representation. In Proceedings of the 7th International Conference on Intelligent Computing: Bio-Inspired Computing and Applications (Zhengzhou, China) (ICIC'11). Springer-Verlag, Berlin, Heidelberg, 223--230. Google ScholarDigital Library
- Mauricio GC Resende, Celso C Ribeiro, Fred Glover, and Rafael Martí. 2010. Scatter search and path-relinking: Fundamentals, advances, and applications. In Handbook of metaheuristics. Springer, Boston, MA, 87--107.Google Scholar
- Michele Samorani, Yang Wang, Zhipeng Lv, and Fred Glover. 2019. Clustering-driven evolutionary algorithms: an application of path relinking to the quadratic unconstrained binary optimization problem. Journal of Heuristics 25, 4 (2019), 629--642.Google ScholarDigital Library
- Vicente P Soloviev, Concha Bielza, and Pedro Larranaga. 2021. Quantum-Inspired Estimation Of Distribution Algorithm To Solve The Travelling Salesman Problem. In 2021 IEEE Congress on Evolutionary Computation (CEC). IEEE, Kraków, Poland, 416--425.Google Scholar
- Kenneth Sorensen, Marc Sevaux, and Fred Glover. 2017. A History of Metaheuristics. Google ScholarCross Ref
- Jirayu Supasil, Poramet Pathumsoot, and Sujin Suwanna. 2021. Simulation of implementable quantum-assisted genetic algorithm. In Journal of Physics: Conference Series, Vol. 1719. IOP Publishing, Trang, Thailand, Article 012102.Google Scholar
- Paolo Toth and Daniele Vigo (Eds.). 2001. The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, USA.Google Scholar
- Anant J Umbarkar and Pranali D Sheth. 2015. Crossover operators in genetic algorithms: a review. ICTACT journal on soft computing 6 (2015), Article 1.Google Scholar
- Yang Wang, Zhipeng Lü, Fred Glover, and Jin-Kao Hao. 2012. Path relinking for unconstrained binary quadratic programming. European Journal of Operational Research 223 (12 2012), 595--604. Google ScholarCross Ref
- Ryota Yasudo, Koji Nakano, Yasuaki Ito, Masaru Tatekawa, Ryota Katsuki, Takashi Yazane, and Yoko Inaba. 2020. Adaptive Bulk Search: Solving Quadratic Unconstrained Binary Optimization Problems on Multiple GPUs. In 49th International Conference on Parallel Processing - ICPP (Edmonton, AB, Canada) (ICPP '20). Association for Computing Machinery, New York, NY, USA, Article 62, 11 pages. Google ScholarDigital Library
- Kouki Yonaga, Masamichi J. Miyama, and Masayuki Ohzeki. 2020. Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer. Google ScholarCross Ref
- Farah Ayiesya Zainuddin, Md Fahmi Abd Samad, and Durian Tunggal. 2020. A review of crossover methods and problem representation of genetic algorithm in recent engineering applications. International Journal of Advanced Science and Technology 29, 6s (2020), 759--769.Google Scholar
- Oylum Şeker, Neda Tanoumand, and Merve Bodur. 2020. Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis. Google ScholarCross Ref
Index Terms
- Comparing Solution Combination Techniques in Scatter Search for Quadratic Unconstrained Binary Optimization
Recommendations
A scatter search approach for the minimum sum-of-squares clustering problem
A metaheuristic procedure based on the scatter search approach is proposed for the non-hierarchical clustering problem under the criterion of minimum sum-of-squares clustering. This algorithm incorporates procedures based on different strategies, such ...
Probabilistic GRASP-Tabu Search algorithms for the UBQP problem
This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by ...
Scatter search for minimizing weighted tardiness in a single machine scheduling with setups
Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent ...
Comments