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2024-06-15 22:10| 来源: 网络整理| 查看: 265

Problem Description

The problem is to change the position and angle of a cannon to fire a projectile as far as possible beyond a wall. The cannon has a muzzle velocity of 300 m/s. The wall is 20 m high. If the cannon is too close to the wall, it fires at too steep an angle, and the projectile does not travel far enough. If the cannon is too far from the wall, the projectile does not travel far enough. For full problem details, see Optimize ODEs in Parallel (Global Optimization Toolbox) or the latter part of the video Surrogate Optimization.

MATLAB Problem Formulation

To solve the problem, call the patternsearch solver from Global Optimization Toolbox. The objective function is in the cannonobjective helper function, which calculates the distance the projectile lands beyond the wall for a given position and angle. The constraint is in the cannonconstraint helper function, which calculates whether the projectile hits the wall, or even reaches the wall before hitting the ground. The helper functions are in separate files that you can view when you run this example.

Set the following inputs for the patternsearch solver. Note that, to use Parallel Computing Toolbox, you must set 'UseParallel' to true in the optimization options.

lb = [-200;0.05]; ub = [-1;pi/2-.05]; x0 = [-30,pi/3]; opts = optimoptions('patternsearch',... 'UseCompletePoll', true, ... 'Display','off',... 'UseParallel',true); % No linear constraints, so set these inputs to empty: A = []; b = []; Aeq = []; beq = [];

Solve on Process-Based Pool

For comparison, solve the problem on a process-based parallel pool first.

Start a parallel pool of process workers.

p = parpool('Processes');Starting parallel pool (parpool) using the 'Processes' profile ... Connected to the parallel pool (number of workers: 6).

To reproduce the same computations later, seed the random generator with the default value.

rng default;

Use a loop to solve the problem several times and average the results.

tProcesses = zeros(5,1); for repetition = 1:numel(tProcesses) tic [xsolution,distance,eflag,outpt] = patternsearch(@cannonobjective,x0, ... A,b,Aeq,beq,lb,ub,@cannonconstraint,opts); tProcesses(repetition) = toc; end tProcesses = mean(tProcesses)tProcesses = 2.7677

To prepare for the comparison with a thread-based pool, delete the current parallel pool.

delete(p);

Solve on Thread-Based Pool

Start a parallel pool of thread workers.

p = parpool('Threads');Starting parallel pool (parpool) using the 'Threads' profile ... Connected to the parallel pool (number of workers: 6).

Restore the random number generator to default settings and run the same code as before.

rng default tThreads = zeros(5,1); for repetition = 1:numel(tThreads) tic [xsolution,distance,eflag,outpt] = patternsearch(@cannonobjective,x0, ... A,b,Aeq,beq,lb,ub,@cannonconstraint,opts); tThreads(repetition) = toc; end tThreads = mean(tThreads)tThreads = 1.5790

Compare the performance of thread workers and process workers.

fprintf('In this example, thread workers are %.2fx faster than process workers.\n', tProcesses/tThreads)In this example, thread workers are 1.75x faster than process workers.

Notice the performance gain due to the optimizations of the thread-based pool.

When you are done with computations, delete the parallel pool.

delete(p);

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