Faster Bi-Objective Non-Dominated Sorting with O(N log N) Complexity

[richardcsuwandi]

This PR introduces a faster non-dominated sorting algorithm that leverages geometric properties to reduce complexity from O(N^2) to O(N log N), resulting in up to 60.92x faster performance for bi-objective problems.

Before (O(N^2) for all cases):

# Original algorithm for all objective counts
for i in range(n):
    for j in range(i + 1, n):
        rel = M[i, j]  # Full dominance matrix calculation
        if rel == 1:
            is_dominating[i].append(j)
            n_dominated[j] += 1
        elif rel == -1:
            is_dominating[j].append(i)
            n_dominated[i] += 1

After (O(N log N) for bi-objective, O(N^2) for others):

# Specialized algorithm for bi-objective problems
if n_objectives == 2:
    return _fast_biobjective_nondominated_sort(F)  # O(N log N) algorithm
else:
    # Fall back to optimized original approach for multi-objective

📊 Performance Results

Size	Original (s)	Evolved (s)	Speedup
50	0.000328	0.000036	9.00x
100	0.001024	0.000078	13.18x
500	0.034089	0.000842	40.49x
1000	0.104040	0.002246	46.33x
2000	0.278000	0.004547	60.92x

Average speedup: 33.98x

Added comprehensive performance test (test_comparison.py) that:

• Uses the same interface as the original pymoo implementation
• Tests with actual bi-objective optimization scenarios
• Verifies identical results between original and optimized methods
• Demonstrates performance improvements across multiple problem sizes