Evolutionary Optimization Strategy Design

Research Question

Design a novel combination of selection, crossover, and mutation operators (and/or a novel evolutionary loop) for continuous black-box optimization that outperforms standard approaches across multiple benchmark functions.

Background

Evolutionary algorithms (EAs) are population-based metaheuristics for black-box optimization. The three core operators — selection, crossover, and mutation — together with the overall evolutionary loop design, determine an EA's performance. Standard approaches include:

• Genetic Algorithms (GA): Tournament selection + Simulated Binary Crossover (SBX) + Polynomial Mutation
• CMA-ES: Adapts the covariance matrix of a multivariate Gaussian to guide search
• Differential Evolution (DE): Uses vector differences between population members for mutation

Each has strengths on different function landscapes (multimodal, ill-conditioned, high-dimensional), but no single strategy dominates all.

Task

Modify the editable section of custom_evolution.py (lines 87-225) to implement a novel or improved evolutionary strategy. You may modify:

• custom_select(population, k, toolbox) — selection operator
• custom_crossover(ind1, ind2) — crossover/recombination operator
• custom_mutate(individual, lo, hi) — mutation operator
• run_evolution(...) — the full evolutionary loop (you can restructure the algorithm entirely)

The DEAP library (deap.base, deap.creator, deap.tools) is available. You may also use numpy, scipy, math, and random.

Interface

• Individuals: Lists of floats, each with a .fitness.values attribute (tuple of one float for minimization).
• run_evolution must return (best_individual, fitness_history) where fitness_history is a list of best fitness per generation.
• TRAIN_METRICS: Print TRAIN_METRICS gen=G best_fitness=F avg_fitness=A periodically (every 50 generations).
• Respect the function signature and return types — the evaluation harness below the editable section is fixed.

Evaluation

Strategies are evaluated on 4 benchmarks (all minimization, lower is better):

Metrics: best_fitness (final best value, lower is better) and convergence_gen (generation reaching near-final fitness).