Binh-Korn
Problem definition
Objective function
f = @(x) [4*sum(x.^2,2), ... sum((x-5).^2,2)]
Optimization settings
o = struct% initializing struct
g1 = @(x) 25 - (x(:,1)-5).^2 - x(:,2).^2 g2 = @(x) (x(:,1)-8).^2 + (x(:,2)+3).^2 - 7.7 o.g = @(x) g1(x).*(g1(x)<0) + g2(x).*(g2(x)<0)% constraints
o.d = 2% dimension of decision variable
o.lb = [0 0]% lower bounds
o.ub = [5 3]% upper bounds
Problem properties
dimension | objectives | smoothness |
2 | 2 | 0 |
Optimization example with nsga2
Algorithm options
o.maxit = 6% 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
optimview('nsga2',info)
References
[1] Binh, T. and U. Korn, "MOBES: A multiobjective evolution strategy for constrained optimization problems.
In Proceedings of the third international Conference on Genetic Algorithms (Mendel97), ", Brno,
Czech Republic, pp. 176-182, 1997