Moead

MOEA/D Skill

Paper: Zhang & Li, "MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition", IEEE TEC 2007.

1. Method Essence

MOEA/D decomposes a multi-objective problem into N single-objective sub-problems: each sub-problem is defined by a weight vector + aggregation function (weighted sum / Tchebycheff), and the entire population = a set of uniformly distributed weight vectors. Core mechanisms:

• Sub-problem division: Each weight vector corresponds to a direction on the front; the population collectively covers the entire front
• Neighborhood collaboration: Each sub-problem exchanges information only with its T nearest weight vectors (neighbors) — crossover/mutation occurs mainly between neighboring sub-problems, replacing global pairing
• Aggregation function: Tchebycheff max_i w_i |f_i - z_i| (z is reference point) is effective for non-convex fronts and is commonly used
• Update rule: If a new individual improves the aggregation value for its sub-problem, it replaces that sub-problem and its neighbors' solutions

2. Recommended Parameters

See params.yaml in this directory for the recommended parameter configuration.

Note: The number of objectives is determined by the length of objective_metrics. Weight vectors are generated in this dimensional space.

What Happens During Evolution

1. Generate uniform weight vectors in objective space
2. Initialize population (one solution per weight vector)
3. Each generation:
   • For each sub-problem (weight vector):
     • Select parents from neighborhood
     • Generate offspring via LLM operators
     • Evaluate offspring
     • Update sub-problem and neighbors if offspring improves aggregation
4. Weight vectors define search directions; population covers the front uniformly
5. Final front is the set of best solutions for each weight vector

Common Pitfalls

• Front has gaps → increase population_size (more weight vectors)
• Convergence uneven → check weight vector distribution; some directions may be harder
• All solutions clustered → reduce neighborhood size T for more local search
• Non-convex front → Tchebycheff aggregation works better than weighted sum

4. Acceptance Criteria

• Weight vectors uniformly distributed in objective space
• Each sub-problem has a corresponding solution on the front
• Front covers all weight vector directions (no missing regions)
• Neighborhood collaboration visible (solutions from nearby weights share features)
• Final front represents the full trade-off surface