Evolutionary Algorithms for Two Problems from the Calculus of Variations

Abstract. A brachistochrone is the path along which a weighted particle falls most quickly from one point to another, and a catenary is the smooth curve connecting two points whose surface of revolution has minimum area. Two evolutionary algorithms find piecewise linear curves that closely approximate brachistochrones and catenaries. Two classic problems in the calculus of variations seek a brachistochrone, the path along which a weighted particle falls most quickly from one point to another, and a catenary, the smooth curve of arc length l between two points whose surface of revolution has minimum area. Analytical solutions to these problems have long been known. In a uniform gravitational field and without friction, a brachistochrone is an arc of a cycloid, the curve traced by a point on a rolling circle. The curve of specified length whose surface of revolution has minimum area is a catenary, an arc of a hyperbolic cosine. Two evolutionary algorithms seek approximate solutions to...

• Type: Conference
• Year: 2003
• Where: GECCO
• Authors: Bryant A. Julstrom
• Keywords: Brachistochrone, GECCO 2003, Minimum Area, Weighted Particle