Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1233.90253
Zamirian, M.; Kamyad, A.V.; Farahi, M.H.
A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation. (English)
[J] Phys. Lett., A 373, No. 38, 3439-3449 (2009). ISSN 0375-9601

Summary: In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.

MSC 2000:: *90C29 Multi-objective programming, etc.
90C30 Nonlinear programming
93C10 Nonlinear control systems
62C86
91B06 Decision theory
65K10 Optimization techniques (numerical methods)

Keywords: optimal path planning; multi-objective dynamic optimization; fuzzy aggregation; parametrization method; non-linear programming; membership function

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]