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

Related functions

nsga2 | plot | scatter