Neural Optimizer: Deep Learning for Combinatorial Optimization

📄 Research Paper

Title: Neural Optimizer: Deep Learning Approaches for Combinatorial Optimization

Authors: Zhang Wei, Li Ming, Wang Xiaoli

Conference: ICML 2024 (International Conference on Machine Learning)

Abstract: This work presents a novel neural architecture for solving combinatorial optimization problems. Our approach combines graph neural networks with reinforcement learning to achieve state-of-the-art performance on various optimization benchmarks.

Key Contributions:

Novel GNN architecture for optimization problems
Reinforcement learning framework for solution search
15% improvement over previous methods on TSP benchmarks
Generalization across different problem sizes

🎯 Key Results

15%

Performance improvement over state-of-the-art

10x

Faster convergence compared to traditional methods

5+

Benchmark datasets evaluated on

🔬 Experimental Results

Comprehensive evaluation across multiple optimization problems and datasets.

Traveling Salesman Problem

Achieved 15% improvement on TSPLIB benchmarks with up to 1000 cities.

Vehicle Routing Problem

Reduced total route distance by 12% on standard VRP datasets.

Job Shop Scheduling

Improved makespan by 18% on benchmark scheduling instances.

Graph Coloring

Found optimal colorings for 95% of test graphs within time limit.

Knapsack Problem

Achieved optimal solutions for 98% of large-scale knapsack instances.

Bin Packing

Reduced number of bins by 8% compared to best known heuristics.

📊 Detailed Analysis

Training Methodology

Our neural optimizer was trained on a diverse set of optimization problems using:

Graph Neural Networks: Custom architecture with attention mechanisms
Reinforcement Learning: Policy gradient methods with curriculum learning
Multi-task Learning: Joint training across different problem types

Performance Comparison

Method	TSP-100	TSP-500	TSP-1000	Training Time
Nearest Neighbor	12.3	15.8	18.2	-
Genetic Algorithm	8.7	11.2	14.1	-
Previous Neural Method	7.2	9.8	12.5	24h
Our Method	6.1	8.3	10.6	18h

Ablation Studies

We conducted extensive ablation studies to understand the contribution of each component:

GNN Architecture: 8% performance gain
Attention Mechanism: 4% performance gain
Curriculum Learning: 3% performance gain

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