Prompt Title: Python

Sure, I can help you with that! Let's start by defining the representation for a solution to the scheduling problem. We will use a list of tuples, where each tuple represents an exam and contains information about its course, time slot, and exam hall.

Here's the code for the representation:

pythonCopy code
# Representation of a solution to the scheduling problem
# A solution is a list of tuples, where each tuple represents an exam
# and contains information about its course, time slot, and exam hall

solution = [(course1, time_slot1, exam_hall1), (course2, time_slot2, exam_hall2), ...]

Next, let's write a function to calculate the fitness of a solution. The fitness function should take a solution as input and output a score indicating how good the solution is. A good solution is one that satisfies all the constraints of the problem and minimizes the total number of conflicts between exams.

Here's the code for the fitness function:

pythonCopy code
def calculate_fitness(solution):
    # Initialize penalty for exceeding maximum usage time for exam hall
    exam_hall_penalty = 10
    
    # Initialize penalty for conflicting student pairs scheduled at the same time
    student_conflict_penalty = 100
    
    # Initialize conflicts counter
    conflicts = 0
    
    # Initialize usage time for each exam hall
    usage_time = {exam_hall: 0 for exam_hall in exam_halls}
    
    # Check for conflicts and update usage time for each exam hall
    for i in range(len(solution)):
        course_i, time_slot_i, exam_hall_i = solution[i]
        usage_time[exam_hall_i] += time_slot_hours[time_slot_i]
        
        for j in range(i+1, len(solution)):
            course_j, time_slot_j, exam_hall_j = solution[j]
            
            # Check for conflicts between courses
            if (course_i, course_j) in conflicting_courses:
                if time_slot_i == time_slot_j and exam_hall_i == exam_hall_j:
                    conflicts += 1
                    
            # Check for conflicts between students
            if (course_i, course_j) in conflicting_students:
                if time_slot_i == time_slot_j and exam_hall_i == exam_hall_j:
                    conflicts += 1
                    
    # Calculate penalty for exceeding maximum usage time for each exam hall
    for exam_hall in exam_halls:
        if usage_time[exam_hall] > max_usage_time:
            conflicts += exam_hall_penalty * (usage_time[exam_hall] - max_usage_time)
            
    # Calculate fitness score
    fitness = conflicts
    
    return fitness

Now, let's implement a genetic algorithm to search for a good solution. Our implementation will include functions for initializing a population of solutions, selecting parents for crossover, performing crossover and mutation, and evaluating the fitness of the resulting offspring. We will experiment with different parameter settings to find the best combination.

Here's the code for the genetic algorithm:

pythonCopy code
import random

# Genetic algorithm parameters
POPULATION_SIZE = 100
TOURNAMENT_SIZE = 5
CROSSOVER_PROBABILITY = 0.8
MUTATION_PROBABILITY = 0.1
MAX_GENERATIONS = 100

# Initialize a population of solutions
def initialize_population(num_courses, num_time_slots, num_exam_halls, population_size):
    population = []
    for i in range(population_size):
        solution = []
        for j in range(num_courses):
            course = j + 1
            time_slot = random.randint(1, num_time_slots)
            exam_hall = random.randint(1, num_exam_halls