Genetic Algorithm for Job Shop Scheduling That Minimises Total Completion Time

Project info

• Field of studyIndustrial Engineering and Production
• LevelDoctoral dissertation (S3)
• Method typeOptimisation
• Estimated build time± 7 working days
• Toolsnumpy (implementasi manual GA); matplotlib
• PriceUS$31 - US$200

Research goal

Optimise makespan by tuning number of jobs and number of machines with Genetic Algorithm.

Variables

Example result

• 17.137Best objective
• 17.137Global optimum
• 0Gap to optimum %
• 100Improvement %
• 24Population size
• 22Generations

The genetic algorithm (population 24, 22 generations) minimises Makespan down to 17.14 at Number of jobs = 17.82 and Number of machines = 39.23, within 0.00% of the global optimum.

Computed from illustrative synthetic data, not from a real study.

About Genetic Algorithm

A genetic algorithm searches for optimal solutions by imitating evolution: selection, crossover, and mutation on a population of solutions. It suits nonlinear or combinatorial optimisation problems that are hard for gradient methods.

Steps

1. 1Define the objective function and variable bounds
2. 2Generate a random initial population
3. 3Compute fitness and select parents (tournament)
4. 4Apply crossover and mutation, keeping the best individual (elitism)
5. 5Repeat until the maximum generation or convergence
6. 6Plot the convergence curve and report the best solution

Assumptions to check

• The objective function is cheap to evaluate
• Parameters (population, mutation, generations) are tuned adequately
• There is no guarantee of the global optimum, so run several times

Reading and reporting the results

Report GA parameters, the best solution, objective value, and convergence curves from several runs with different seeds. Compare with other methods to show solution quality.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt

def rastrigin(p):
    return 20 + (p ** 2 - 10 * np.cos(2 * np.pi * p)).sum(axis=1)

rng = np.random.default_rng(31)
dim, pop_n, gens = 2, 60, 80
lo, hi = -5.12, 5.12
number_of_jobs = rng.uniform(lo, hi, (pop_n, dim))      # population
best_hist = []
for g in range(gens):
    makespan = rastrigin(number_of_jobs)                   # cost (to minimise)
    best_hist.append(makespan.min())
    elite = number_of_jobs[makespan.argmin()].copy()
    # tournament selection
    idx = rng.integers(0, pop_n, (pop_n, 2))
    win = np.where(makespan[idx[:, 0]] < makespan[idx[:, 1]], idx[:, 0], idx[:, 1])
    parents = number_of_jobs[win]
    # blend crossover
    mates = parents[rng.permutation(pop_n)]
    alpha = rng.random((pop_n, 1))
    child = alpha * parents + (1 - alpha) * mates
    # gaussian mutation
    mask = rng.random(child.shape) < 0.1
    child = child + mask * rng.normal(0, 0.3, child.shape)
    child = np.clip(child, lo, hi)
    child[0] = elite
    number_of_jobs = child

final = rastrigin(number_of_jobs)
print("Best cost:", round(final.min(), 5))
print("Best solution:", number_of_jobs[final.argmin()].round(4))

plt.plot(best_hist)
plt.xlabel("Generation"); plt.ylabel("Best cost")
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions