Simulated Annealing for Optimising running efficiency in middle-distance runners by Tuning training distance and rest days

Project info

• Field of studySports and Kinesiology
• LevelDoctoral dissertation (S3)
• Method typeOptimisation
• Estimated build time± 7 working days
• Toolsnumpy (implementasi manual); scipy.optimize.dual_annealing sebagai pembanding
• PriceUS$31 - US$197

Research goal

Find settings of training distance and rest days that optimise running efficiency in middle-distance runners with simulated annealing and a cooling schedule.

Variables

Example result

• 47.6Best objective
• 47.579Global optimum
• 0.044Gap to optimum %
• 0.566Acceptance ratio
• 500Iterations
• 0.081Final temperature

Simulated annealing (500 iterations) lowers running efficiency to 47.60 at training distance = 185.57 and rest days = 16.87; 56.6% of moves were accepted and the gap to the optimum is 0.04%.

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

About Simulated Annealing

Simulated annealing explores the solution space by accepting worse moves with a probability that falls as temperature decreases. It suits global optimisation of functions with many local minima and combinatorial problems.

Steps

1. 1Define the objective, bounds, and starting point
2. 2Set the initial temperature and cooling schedule
3. 3Generate a random neighbour solution
4. 4Accept if better, or with probability exp(-delta/T) if worse
5. 5Lower the temperature and repeat
6. 6Plot the objective trajectory and report the best solution

Assumptions to check

• The cooling schedule is slow enough to avoid local minima
• The neighbour step matches the problem scale
• Several runs with different seeds assess consistency

Reading and reporting the results

Report the initial temperature, cooling rate, best solution and objective value, and their variation across runs. Explain that results are heuristic with no guarantee of the global optimum.

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
from scipy.optimize import dual_annealing

def f(p):
    return (p[0] ** 2 + p[1] ** 2) / 10 + 3 * (2 - np.cos(2 * p[0]) - np.cos(2 * p[1]))

rng = np.random.default_rng(32)
training_distance = rng.uniform(-5, 5, 2)          # current solution
cur = f(training_distance)
best_x, best = training_distance.copy(), cur
T, cooling = 5.0, 0.995
running_efficiency = []                              # objective trajectory
for it in range(4000):
    cand = np.clip(training_distance + rng.normal(0, 0.5, 2), -5, 5)
    fc = f(cand)
    if fc < cur or rng.random() < np.exp(-(fc - cur) / T):
        training_distance, cur = cand, fc
        if cur < best:
            best_x, best = training_distance.copy(), cur
    running_efficiency.append(best)
    T *= cooling

print("SA best x:", best_x.round(4), "f =", round(best, 5))
ref = dual_annealing(f, bounds=[(-5, 5), (-5, 5)], seed=32)
print("scipy dual_annealing:", ref.x.round(4), "f =", round(ref.fun, 5))

plt.plot(running_efficiency)
plt.xlabel("Iteration"); plt.ylabel("Best objective")
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