Solving Method for Multi-level Programming Problems Based on Gravity Search Algorithm

The researches on multi-level programming models have gradually become one of the most promising research fields in operational research, and have been widely used in many fields. In this paper the theoretical background, basic definitions, and basic properties of multi-level programming models are introduced. Then, the basic principles, basic models, solution processes and characteristics of gravity search algorithm are introduced in detail. Taking a bi-level programming model as an example, the basic method of solving multi-level programming problem is proposed based on gravity search algorithm. In order to verify the validity and the feasibility of the proposed solving method, the multiple test functions, including continuous linear bi-level programming problem, integer linear bi-level programming problem and nonlinear bi-level programming problems, are used to investigate the performances of gravity search algorithm to solve multi-level programming models. The results show the high performances of the proposed method.

[1]  Surabhi Sinha.  Fuzzy mathematical programming applied to multi-level programming problems , 2003, Comput. Oper. Res..

[2]  Abhishek Dwivedi,et al.  Bi-level and Multi-Level Programming Problems: Taxonomy of Literature Review and Research Issues , 2017, Archives of Computational Methods in Engineering.

[3]  G. Anandalingam,et al.  Multi-level programming and conflict resolution , 1991 .

[4]  Wei Wang,et al.  Cooperative planning model of renewable energy sources and energy storage units in active distribution systems: A bi-level model and Pareto analysis , 2019, Energy.

[5]  Zhu Hong-bo.  Architecture Design for Heterogeneous Multimedia Mesh Networks and Research on Cross-Layer QoS Routing Algorithm , 2010 .

[6]  S. B. Sinha,et al.  A linear programming approach for linear multi-level programming problems , 2004, J. Oper. Res. Soc..

[7]  M. Zhou,et al.  A bi-level probabilistic transmission planning with intermittent generations based on life cycle cost , 2017 .

[8]  Seyed Parsa Parvasi,et al.  A bi-level school bus routing problem with bus stops selection and possibility of demand outsourcing , 2017, Appl. Soft Comput..

[9]  Zhao Tong,et al.  A Bi-Level Programming Model and Solution Algorithm on Optimal Parameter Setting in Wireless Sensor Networks , 2007 .

[10]  Yao Min.  UAVs 3-D Cooperative Attack Path Planning by Turns Based on Grid Model and Bi-Level Programming , 2011 .

[11]  Bo Sun,et al.  Bi-level programming model for multi-modal regional bus timetable and vehicle dispatch with stochastic travel time , 2016, Cluster Computing.

[12]  Wang Qing-yun.  Tri-level programming model for optimization of regional transportation corridor layout , 2010 .

[13]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[14]  Liu Wei,et al.  Smooth path planning for unmanned aerial vehicles in unknown complex environments , 2012 .

[15]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[16]  Hejun Xuan,et al.  New bi-level programming model for routing and spectrum assignment in elastic optical network , 2017 .

[17]  Miguel Angel Sanz-Bobi,et al.  Profit-maximization generation maintenance scheduling through bi-level programming , 2018, Eur. J. Oper. Res..

[18]  Mostafa Zandieh,et al.  A bi-level programming approach for production-distribution supply chain problem , 2017, Comput. Ind. Eng..

[19]  Ue-Pyng Wen,et al.  Linear Bi-level Programming Problems — A Review , 1991 .

[20]  Serhat Duman,et al.  Optimal power flow using gravitational search algorithm , 2012 .

[21]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..