Grasp Hsc09
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Accelerate PSO algorithm using gradients by automatic differentiation technique
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Grasp Hsc09
- 1. GRASP – Gr adient- a ided S warm O p timization C. D. Bocaniala and V. V. S. S. Sastry Department of Engineering Systems and Management, Cranfield University, Shrivenham, SN6 8LA, UK {cbocaniala.cu, vsastry.cu}@defenceacademy.mod.uk
- 2. Motivation
- 3. Motivation
- 4. Intersection of gradient half-lines
- 5. Motivation
- 6. Algorithm while not(stop_conditions) perform alternatively EITHER intersection of gradient half-lines OR Broyden–Fletcher–Goldfarb–Shanno (BFGS) end
- 11. F1 3 – Shifte d Ex p a n d e d G r i ew a nk ’ s p lus Ro s en b roc k function; 10D, 77,282 vs 100,000
Hinweis der Redaktion
- GRASP brings together core ideas from Particle Swarm Optimization and gradient-based optimization methods.
- The figure displays the contour plot in 2D of function F12 from CEC2005 benchmark. It shown the initial search directions corresponding to a fine grid defined on the search space. The directions DO NOT correspond to the natural form of the underlying surface!
- The figure presents the reverted gradients (pointing to the nearest local minima) for the previous function. Please note that the search directions DO correspond to the natural form of the underlying surface!
- The sketch presents the intersection between the gradient half-lines of a particle, its corresponding personal best particle and the global best particle. The sketch also depicts the way PSO decides the new search direction for the very same particle, its personal best and global best. In higher dimensional spaces, the intersection between two gradient half-lines is defined as the closest pair of points on the two half-lines.
- The figure presents the set of points (black) whose gradient half-lines intersect (blue) the gradient half-line of a chosen point (red). Please note that in this particular case most of the points that present intersection with the chosen gradient half-line are being drawn towards more advantageous positions. All the black points are like attractor regions. They are the points for which there is an intersection point for the half-lines. See F12
- exclude F8