rcgapy is a python implemented real coded genetic algorithm [1] to find good local optima for any linear or nonlinear functions with linear, nonlinear and integer constraints.
rcgapy simply depends on numpy and numba for numerical computations and matplotlib for visualization. Just run the following command to get started.
pip install -r requirements.txt
In main.py, there is an example how to minimize a nonlinear objective function subject to linear, nonlinear
and integer constraints.
A few steps are required to model the problem.
- The objective function can be expressed as:
@njit(fastmath=True)
def objective_function(x):
r = (x[0] - 1.) ** 2 + (x[1] - 2.) ** 2 + (x[2] - 3.) ** 2 + (x[3] - 1.) ** 2 + (x[4] - 1.) ** 2 + \
(x[5] - 1.) ** 2 - np.log(x[6] + 1.)
return r- All nonlinear constraints are required to be written into a single function
@njit(fastmath=True)
def nonlinear_functions(x):
const1 = x[5] ** 2 + x[0] ** 2 + x[1] ** 2 + x[2] ** 2 - 5.5
const2 = x[1] ** 2 + x[4] ** 2 - 1.64
const3 = x[2] ** 2 + x[5] ** 2 - 4.25
const4 = x[2] ** 2 + x[4] ** 2 - 4.64
return const1, const2, const3, const4- Type of decision variables (real or integer)
x_cts = np.array([0, 1, 2]) # index of continuous variables
x_int = np.array([3, 4, 5, 6]) # index of integer variables- Bounds of each decision variable
lb_cts = np.array([0., 0., 0.]) # lower bound of continuous variables
ub_cts = np.array([1.2, 1.8, 2.5]) # upper bound of continuous variables
lb_int = np.array([0, 0, 0, 0]) # lower bound of integer variables
ub_int = np.array([1, 1, 1, 1]) # upper bound of integer variables- Coefficients of linear constraints
lin_rhs = np.array([[5., 1.2, 1.8, 2.5, 1.2]]).T # right-hand side of linear inequality constraints
lin_lhs = np.array([ # left-hand side of linear inequality constraints
[1., 1., 1., 1., 1., 1., 0.],
[1., 0., 0., 1., 0., 0., 0.],
[0., 1., 0., 0., 1., 0., 0.],
[0., 0., 1., 0., 0., 1., 0.],
[1., 0., 0., 0., 0., 0., 1.]
])Now we are done with the problem setup, just call the opt function to run
# optimize
start = time.perf_counter()
best_obj, best_ind, avg_fit, best_fit, violation = opt(objective_function, x_cts, x_int, lb_cts, ub_cts, lb_int, ub_int,
lin_lhs, lin_rhs, nonlinear_functions)
global_best_obj = 3.557463
print(f"Gap: {np.round((best_obj - global_best_obj) / global_best_obj, 6)}, total violation: {violation}")
print(f"GA takes {time.perf_counter() - start} seconds to execute. ")The average fitness and best fitness value in each generation can be visualized by just one line of code:
animation = ga_dynamic_single(avg_fit, best_fit)In demo.py, there is a visualization of the population evolving process on the peaks function