Abstract
This paper proposes a neurodynamic approach for solving the quadratic zero-one programming problem with linear constraints. Based on the basic idea of the Scholtes’ relaxation scheme, the original quadratic zero-one programming problem can be approximated by a parameterized nonlinear program. Then, an artificial neural network is proposed to solve the related parameterized nonlinear programming. It is certified that the presented artificial neural network is stable in the sense of Lyapunov. Some numerical experiments are introduced to illustrate our results in the end.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Billionnet, A., Costa, M.C., Sutter, A.: An efficient algorithm for a task allocation problem. J. ACM 39(3), 502–518 (1992)
Billionnet, A., Sutter, A.: Persistency in quadratic 0–1 optimization. Math. Program. 54(1–3), 115–119 (1992)
Chen, J.S., Ko, C.H., Pan, S.: A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems. Inf. Sci. 180, 697–711 (2010). Elsevier Science Inc.
Effati, S., Mansoori, A., Eshaghnezhad, M.: An efficient projection neural network for solving bilinear programming problems. Neurocomputing 168(C), 1188–1197 (2015)
Feng, J., Ma, Q., Qin, S.: Exponential stability of periodic solution for impulsive memristor-based cohen-grossberg neural networks with mixed delays. Int. J. Pattern Recognit Artif Intell. 31(7), 1750022 (2017)
Hoheisel, T., Kanzow, C., Schwartz, A.: Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math. Program. 137(1–2), 257–288 (2013)
Krarup, J., Pisinger, D., Plastria, F.: Discrete location problems with push–pull objectives. Discret. Appl. Math. 123(1), 363–378 (2002)
Nazemi, A.R.: A dynamic system model for solving convex nonlinear optimization problems. Commun. Nonlinear Sci. Numer. Simul. 17(4), 1696–1705 (2012)
Pardalos, P.M., Rodgers, G.P.: Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45(2), 131–144 (1990)
Qin, S., Yang, X., Xue, X., Song, J.: A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints. IEEE Trans. Cybern. 47(10), 3063–3074 (2017)
Qin, S., Xue, X.: A two-layer recurrent neural network for nonsmooth convex optimization problems. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1149 (2015)
Ranjbar, M., Effati, S., Miri, S.M.: An artificial neural network for solving quadratic zero-one programming problems. Neurocomputing 235, 192–198 (2017)
Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discret. Math. 3(3), 411–430 (2006)
Tank, D.W., Hopfield, J.J.: Simple ‘neural’ optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circ. Syst. 33(5), 533–541 (1986)
Vidyasagar, M.: Minimum-seeking properties of analog neural networks with multilinear objective functions. IEEE Trans. Autom. Control 40(8), 1359–1375 (1995)
Wang, Y., Cheng, L., Hou, Z.G., Yu, J., Tan, M.: Optimal formation of multirobot systems based on a recurrent neural network. IEEE Trans. Neural Netw. Learn. Syst. 27(2), 322–333 (2016)
Wu, H., Li, R., Yao, R., Zhang, X.: Weak, modified and function projective synchronization of chaotic memristive neural networks with time delays. Neurocomputing 149(PB), 667–676 (2015)
Wu, H., Zhang, X., Xue, S., Wang, L., Wang, Y.: LMI conditions to global Mittag-Leffler stability of fractional-order neural networks with impulses. Neurocomputing 193(c), 148–154 (2016)
Xia, Y., Wang, J.: A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans. Neural Netw. 16(2), 379–386 (2005)
Xia, Y., Wang, J.: A general projection neural network for solving monotone variational inequalities and related optimization problems. IEEE Trans. Neural Netw. 15(2), 318–328 (2004)
Acknowledgments
This research is supported by the National Natural Science Foundation of China (61773136, 11471088) and the NSF project of Shandong province in China with granted No. ZR2014FM023.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Han, W., Yan, S., Wen, X., Qin, S., Li, G. (2018). An Artificial Neural Network for Solving Quadratic Zero-One Programming Problems. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-92537-0_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92536-3
Online ISBN: 978-3-319-92537-0
eBook Packages: Computer ScienceComputer Science (R0)