Hello John,
The Genetic Algorithm (GA) in MATLAB doesn't directly support equality constraints when using integer or binary variables. This is because GA is inherently a heuristic method that doesn't easily handle equality constraints, especially with discrete variables. However, there are some strategies you can use to work around this limitation:
1. Objective Function with Penalty: Modify your objective to include a penalty for violating equality constraints:
\[
\text{Objective} = \text{Original Objective} + \text{penalty} \times \| A_{eq} \cdot x - b_{eq} \|^2
\]
2. Set Up GA: Use `IntCon` for binary variables and include the modified objective function.
Here's a quick example:
function f = objectiveWithPenalty(x)
f_original = ...; % Define your original objective
penalty = 1e6; % Large penalty value
Aeq = ...; % Equality constraint matrix
beq = ...; % Equality constraint vector
penalty_term = penalty * norm(Aeq * x - beq)^2;
f = f_original(x) + penalty_term;
end
options = optimoptions('ga', 'IntCon', 1:n, 'Display', 'iter');
[x, fval] = ga(@objectiveWithPenalty, n, [], [], [], [], lb, ub, [], options);
This approach helps enforce equality constraints by penalizing violations in the objective function.
I hope this helps to resolve your issue.
