Abstract
In this paper, three recently developed meta-heuristic optimization algorithms, known as colliding bodies optimization (CBO), enhanced colliding bodies optimization (ECBO) and tug of war optimization (TWO), are used for optimum nodal ordering to reduce bandwidth, profile and wavefront of sparse matrices. The CBO is a simple optimization method inspired by a collision between two objects in one dimension. Each agent is modeled as a body which has a specified mass and velocity. A collision occurs between pairs of bodies, and the new positions of the colliding bodies are updated based on the collision laws. The ECBO employs memory to save some best-so-far position to improve the performance of the CBO without increasing the computational effort. This algorithm uses a mechanism to escape from local optima. The recently developed algorithm TWO is a multi-agent meta-heuristic algorithm, which considers each candidate solution as a team engaged in a series of tug of war competitions. The bandwidth, profile and wavefront of some graph matrices, which have equivalent pattern to structural matrices, are minimized utilizing these methods. Comparison of the achieved results with those of some existing approaches shows the robustness of these three new meta-heuristic algorithms for bandwidth, profile and wavefront optimization.
Similar content being viewed by others
References
Bernardes JAB, Oliveira SLGD (2015) A systematic review of heuristics for profile reduction of symmetric matrices. Procedia Comput Sci 51:221–230
Cassell AC, de C Henderson JC, Kaveh A (1974) Cycle bases for the flexibility analysis of structures. Int J Numer Methods Eng 8(3):521–528
Cuthill E, McKee J (1969) Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 24th national conference ACM, Bradon System Press, NJ, p 157–172
Gibbs NE, Poole WG, Stockmeyer PK (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 12:236–250
Kaveh A. (1974) Applications of topology and matroid theory to the analysis of structures. Ph.D. thesis, Imperial College of Science and Technology, London University, UK
Kaveh A (1986) Ordering for bandwidth reduction. Comput Struct 24:413–420
Kaveh A (1992) Recent developments in the force method of structural analysis. Appl Mech Rev 45(9):401–418
Kaveh A (2004) Structural mechanics: graph and matrix methods, 3rd edn. Research Studies Press, Somerset
Kaveh A (2006) Optimal structural analysis, 2nd edn. John Wiley, Chichester
Kaveh A (2014) Advances in Metaheuristic Algorithms for Optimal Design of Structures. Springer International Publishing, Switzerland
Kaveh A, Behzadi AM (1987) An efficient algorithm for nodal ordering of networks. Iranian J Sci Technol 11:11–18
Kaveh A, Bijari Sh (2015) Bandwidth optimization using CBO and ECBO. Asian J Civil Eng 16(4):535–545
Kaveh A, Ilchi Ghazaan M (2014a) Enhanced colliding bodies optimization for design problems with continuous and discrete variables. Adv Eng Softw 77:66–75
Kaveh A, Ilchi Ghazaan M (2014b) Enhanced colliding bodies algorithm for truss optimization with dynamic constraints, J Comput Civil Eng, ASCE 04014104-1411
Kaveh A, Mahdavi VR (2014a) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27
Kaveh A, Mahdavi VR (2014b) Colliding bodies optimization method for optimum design of truss structures with continuous variables. Adv Eng Softw 70:1–12
Kaveh A, Rahami H (2004) Algebraic Graph theory for suboptimal cycle bases of graphs for an efficient force method. Iranian J Sci Technol Trans B: Technol 28:529–536
Kaveh A, Rahimi Bondarabady HAR (2002) A multi-level finite element nodal ordering using algebraic graph theory. Finite Elem Anal Des 38:245–261
Kaveh A, Roosta GR (1997) Graph-theoretical methods for profile reduction. In: Mouchel centenary conference on innovation in civil and structural engineering, Cambridge, UK
Kaveh A, Sharafi P (2009) Nodal ordering for bandwidth reduction using ant system algorithm. Eng Comput 3(26):313–323
Kaveh A, Sharafi P (2012) Ordering for bandwidth and profile minimization problems via charged system search algorithm. Iranian J Sci Technol Trans Civil Eng C1(36):39–52
Kaveh A, Zolghadr A (2016) A novel meta-heuristic algorithm: tug of war optimization. Int J Optim Civil Eng 6:469–493
King IP (1970) An automatic reordering scheme for simultaneous equations derived from network systems. Int J Numer Methods Eng 2:523–533
Koohestani B, Poli R (2014) Addressing the envelope reduction of sparse matrices using a genetic programming system. Comput Optim Appl 60:789–814
Papademetrious CH (1976) The NP-completeness of bandwidth minimization problem. Comput J 16:177–192
Rahimi Bondarabady HA, Kaveh A (2004) Nodal ordering using graph theory and a genetic algorithm. Finite Elem Anal Des 40(9–10):1271–1280
Sloan SW (1986) An algorithm for profile and wavefront reduction of sparse matrices. Int J Number Methods Eng 23:1693–1704
Acknowledgments
The first author is grateful to Iran National Science Foundation for the support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaveh, A., Bijari, S. Bandwidth, Profile and Wavefront Optimization Using PSO, CBO, ECBO and TWO Algorithms. Iran J Sci Technol Trans Civ Eng 41, 1–12 (2017). https://doi.org/10.1007/s40996-016-0026-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-016-0026-z