GRASP – Gradient-aided Swarm Optimization

C. D. Bocaniala and V. V. S. S. SastryDepartment of Engineering Systems and Management,

Cranfield University, Shrivenham, SN6 8LA, UK{cbocaniala.cu, vsastry.cu}@defenceacademy.mod.uk

Motivation

Motivation

Intersection of gradient half-lines

Motivation

Algorithm

while not(stop_conditions)perform alternatively

EITHERintersection of gradient half-lines

ORBroyden–Fletcher–Goldfarb–Shanno (BFGS)

end

Algorithm

• The search is not constrained to a hypercube (initialization range)

• The gradient half-lines intersection technique has NO parameters

• The BFGS has a corresponding set of parameters

Algorithm

• MAD tool used for gradient computation (including inside BFGS)

• BFGS and MAD may be replaced by other toolso MAD dedicated MATLAB toolbox

Benchmark tests• CEC2005

benchmark• 25 functions• Comparison with

Standard PSO 2007 version

• … short demo

F13 – Shifted Expanded Griewank’s plus Rosenbrock function; 10D,77,282 vs 100,000

Concluding Remarks

• GRASP is at its best in higher dimensions• MAD tool overloads a large but not the full

set of MATLAB functions• Replacing BFGS by a parameter-less

gradient-based method – need further analysis

• The computer-implemented version of the objective function and its gradient function