Chakong-Haimes
Problem definition
Objective function
f = @(x) [(x(:,1)-2).^2 + (x(:,2)-1).^2 + 2,...
9*x(:,1) - (x(:,2)-1).^2]
Optimization settings
o = struct% initializing struct
g1 = @(x) 225 - sum(x.^2,2) g2 = @(x) 10 - x(:,1) + 3*x(:,2) o.g = @(x) g1(x).*(g1(x)<0) + g2(x).*(g2(x)<0)% constraints
o.d = 2% dimension of decision variable
o.lb = -20% lower bounds
o.ub = 20% upper bounds
Problem properties
| dimension | objectives | smoothness |
| 2 | 2 | - |
Optimization example with nsga2
Algorithm options
o.maxit = 40% number of iterations
o.pop = 40% number of population
Optimization
rng(0)% for tractability
[popPos,popFront,popCost,popInfo,traceIt] = nsga2(f,o)% running minimization
Animation
rng(0) [~,~,~,~,~,info] = nsga2(f,o) info.plot = 'pareto' info.animate = true% plot animation
info.animfreq = 2% frame frequency
optimview('nsga2',info)
References
[1] V. Chankong, Y.Y. Haimes, "Multiobjective Decision Making Theory and Methodology", Elsevier Science, New York, 1983