Future Trails for Integer Programming and Relations to Artificial Intelligence

Pavlo Romaniuk *

Senior Programmer/Developer, Capgemini America Inc, Ukraine.

*Author to whom correspondence should be addressed.


Abstract

Aims: A review of methods and approaches for solving linear integer problems is presented in this work. These problems are classified as NP-hard optimization algorithms in artificial intelligence.

Study Design: we have used the Google scholar to collect the data resources from past 5 years to analysis the techniques and methods used in different algorithms in artificial intelligence.

Methodology: Exact optimum solution for this class of challenges also need use of substantial computer resources. The current direction in which several researcher focuses their efforts to effectively address numerous difficult practical issues is the creation of efficient hybrid techniques that combine in an appropriate way the finest elements of multiple methods (precise or estimated). The approximation algorithms' core heuristic techniques might be classified as constructive algorithms and local-improvement algorithms.

Results: We examined three artificial intelligence algorithms utilizing the linear integer programming approach. Algorithm based on population It has also been demonstrated that a population of a critical size is necessary for a population-based optimization method to be effective. The genetic algorithm is shown next. The goal value associated with this solution may be utilized to effectively reduce the search tree in bound and branch type integer programming methods. Finally, we analyze the particle swarm optimization (PSO) approach, which demonstrates that In most cases, PSO outperforms the Branch and Bound method in solving such issues quickly. 

Conclusion: In actuality, integer optimization issues describe a wide spectrum of real-world difficulties. Their population and size are constantly growing. Although while accurate methods for integer issues have substantially improved in recent years, their long runtimes and memory needs make them unsuitable for actual medium and large-scale applications.

Keywords: Linear integer programming, artificial intelligence, population based algorithm, genetic algorithm, PSO


How to Cite

Romaniuk, P. (2023). Future Trails for Integer Programming and Relations to Artificial Intelligence. Asian Journal of Research in Computer Science, 15(2), 1–10. https://doi.org/10.9734/ajrcos/2023/v15i2315

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References

Xiao H, Muthu B, Kadry SN. Artificial intelligence with robotics for advanced manufacturing industry using robot-assisted mixed-integer programming model. Intell Serv Robot. 2020;1-10. DOI: 10.1007/s11370-020-00326-7

Liang H, Tsuei M, Abbott N, You F. AI framework with computational box counting and Integer programming removes quantization error in fractal dimension analysis of optical images. Chem Eng J. 2022;446:137058. DOI: 10.1016/j.cej.2022.137058

Kleinert T, Labbé M, Ljubić I, Schmidt M. A survey on mixed-integer programming techniques in bilevel optimization. EURO J Comp Optim. 2021;9:100007. DOI: 10.1016/j.ejco.2021.100007

Valicka CG, Garcia D, Staid A, Watson J-P, Hackebeil G, Rathinam S, et al. Mixed-integer programming models for optimal constellation scheduling given cloud cover uncertainty. Eur J Oper Res. 2019; 275(2):431-45. DOI: 10.1016/j.ejor.2018.11.043

Radoglou-Grammatikis P, Sarigiannidis P, Lagkas T, Moscholios I. A compilation of UAV applications for precision agriculture. Comput Netw. 2020;172:107148. DOI: 10.1016/j.comnet.2020.107148

Wang D, Tan D, Liu L. Particle swarm optimization algorithm: an overview. Soft Comput. 2018;22(2):387-408.

DOI: 10.1007/s00500-016-2474-6

Luo X, Yuan Y, Chen S, Zeng N, Wang Z. Position-transitional particle swarm optimization-incorporated latent factor analysis. IEEE Trans Knowl Data Eng. 2020;34(8):3958-70. DOI: 10.1109/TKDE.2020.3033324

Bengio Y, Lodi A, Prouvost A. Machine learning for combinatorial optimization: A methodological tour d’horizon. Eur J Oper Res. 2021;290(2):405-21. DOI: 10.1016/j.ejor.2020.07.063

Li Z, Chen Q, Koltun V. Combinatorial optimization with graph convolutional networks and guided tree search. Adv Neural Inf Process Syst. 2018;31.

Liang Y, Cheng G. Topology optimization via sequential integer programming and canonical relaxation algorithm. Comput Methods Appl Mech Eng. 2019;348: 64-96. DOI: 10.1016/j.cma.2018.10.050

Hubara I, Nahshan Y, Hanani Y, Banner R, Soudry D. ’Improving post training neural quantization: Layer-wise calibration and integer programming,’ arXiv preprint arXiv:2006.10518; 2020.

Rajeswaran A, Finn C, Kakade SM, Levine S. Meta-learning with implicit gradients. Adv Neural Inf Process Syst. 2019;32.

Huisman M, Van Rijn JN, Plaat A. A survey of deep meta-learning. Artif Intell Rev. 2021;54(6):4483-541. DOI: 10.1007/s10462-021-10004-4

Barman S, Krishnamurthy SK. Approximation algorithms for maximin fair division. ACM Trans Econ Comput. 2020; 8(1):1-28. DOI: 10.1145/3381525

He Y, Chen Y, Lu J, Chen C, Wu G. Scheduling multiple agile earth observation satellites with an edge computing framework and a constructive heuristic algorithm. J Syst Archit. 2019;95:55-66. DOI: 10.1016/j.sysarc.2019.03.005

Mele UJ, Gambardella LM, Montemanni R. A new constructive heuristic driven by machine learning for the traveling salesman problem. Algorithms. 2021; 14(9):267. DOI: 10.3390/a14090267

Hosseini Shirvani MH. A hybrid meta-heuristic algorithm for scientific workflow scheduling in heterogeneous distributed computing systems. Eng Appl Artif Intell. 2020;90:103501. DOI: 10.1016/j.engappai.2020.103501

Wang H, Alidaee B. Effective heuristic for large-scale unrelated parallel machines scheduling problems. Omega. 2019; 83:261-74. DOI: 10.1016/j.omega.2018.07.005

Wu G, Mallipeddi R, Suganthan PN. Ensemble strategies for population-based optimization algorithms–A survey. Swarm Evol Comput. 2019;44:695-711. DOI: 10.1016/j.swevo.2018.08.015

Katoch S, Chauhan SS, Kumar V. A review on genetic algorithm: past, present, and future. Multimedia Tool Appl. 2021; 80(5):8091-126. DOI: 10.1007/s11042-020-10139-6, PMID 33162782.

Ben-Ammar O, Castagliola P, Dolgui A, Hnaien F. A hybrid genetic algorithm for a multilevel assembly replenishment planning problem with stochastic lead times. Comput Ind Eng. 2020;149: 106794. DOI: 10.1016/j.cie.2020.106794

Piotrowski AP, Napiorkowski JJ, Piotrowska AE. Population size in particle swarm optimization. Swarm Evol Comput. 2020;58:100718. DOI: 10.1016/j.swevo.2020.100718

Ren Y, Lu Z, Liu X. A branch-and- bound embedded genetic algorithm for resource-constrained project scheduling problem with resource transfer time of aircraft moving assembly line. Optim Lett. 2020;14(8): 2161-95. DOI: 10.1007/s11590-020-01542-x