[논문 리뷰] Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem

André Hottung, Kevin Tierney|arXiv (Cornell University)|2019. 11. 21.

Vehicle Routing Optimization Methods참고 문헌 31인용 수 60

한 줄 요약

NLNS는 학습된 수리 휴리스틱을 대규모 이웃 탐색에 통합하여 CVRP와 SDVRP를 해결하고 기존 ML 접근법을 능가하며 최첨단 최적화 방법에 근접합니다.

ABSTRACT

Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in recent years, but approaches based purely on machine learning are still outperformed by state-of-the-art optimization methods. To close this performance gap, we propose a novel large neighborhood search (LNS) framework for vehicle routing that integrates learned heuristics for generating new solutions. The learning mechanism is based on a deep neural network with an attention mechanism and has been especially designed to be integrated into an LNS search setting. We evaluate our approach on the capacitated vehicle routing problem (CVRP) and the split delivery vehicle routing problem (SDVRP). On CVRP instances with up to 297 customers, our approach significantly outperforms an LNS that uses only handcrafted heuristics and a well-known heuristic from the literature. Furthermore, we show for the CVRP and the SDVRP that our approach surpasses the performance of existing machine learning approaches and comes close to the performance of state-of-the-art optimization approaches.

연구 동기 및 목표

• VRP 해결 성능 향상을 위해 상위 메타휴리스틱 내에서 학습 기반 휴리스틱의 사용을 촉진한다.
• 큰 이웃 탐색에서 불완전하게 파괴된 해를 다룰 수 있는 신경망 수리 연산자를 개발한다.
• GPU 병렬 처리와 문제에 구애받지 않는 파괴/수리 구성요소를 활용하여 CVRP 및 SDVRP의 확장 가능한 해결을 가능하게 한다.
• NLNS를 첨단 ML 방법과 전통적 최적화 솔루션과 비교 평가하여 성능 향상을 정량화한다.

제안 방법

• NLNS, a large neighborhood search that uses a neural network with attention to repair destroyed VRP solutions.
• Implement two simple destroy operators (point-based and tour-based) to create incomplete solutions.
• Train a neural repair model via policy gradient reinforcement learning to connect ends of incomplete tours under feasibility constraints.
• Use a GPU-accelerated architecture with attention-based embeddings to compute action probabilities for repairing incomplete tours.
• Train repair operators on instance distributions to tailor repairs to specific problem characteristics.
• Evaluate NLNS in batch and single-instance search modes, with comparisons to ML baselines and optimization solvers.

실험 결과

연구 질문

• RQ1 Can NLNSlearned repair operators outperform handcrafted repairs within a large neighborhood search for CVRP/SDVRP?
• RQ2 How does NLNS compare to existing ML approaches (AM, RL-BS) on CVRP/SDVRP in terms of solution quality and runtime?
• RQ3 What is the impact of the destroy/repair design and GPU-accelerated architecture on scalability to larger CVRP/SDVRP instances?
• RQ4 Do learned repairs approach the performance of state-of-the-art optimization methods on CVRP and SDVRP?
• RQ5 How does the batch vs. single-instance search mode affect solution quality and efficiency?

주요 결과

Instance Set	Method	Avg. Cost	Total Time (s)
CVRP	NLNS	6.19	431
CVRP	AM	6.25	451
CVRP	RL-BS	6.40	2*
SDVRP	NLNS	6.15	611
SDVRP	AM	6.25	615
SDVRP	RL-BS	6.34	2*

• NLNS는 CVRP/SDVRP 인스턴스 집합에서 수작업 수리 LNS 및 기존 ML 접근법을 크게 상회한다.
• 최대 100 고객인 CVRP/SDVRP에서 NLNS가 보고된 테스트에서 AM 및 RL-BS보다 더 낮은 평균 비용을 달성한다.
• 배치 NLNS(병렬 인스턴스 해결)는 모든 테스트된 인스턴스 세트(CVRP 및 SDVRP)에서 비교 대상 ML 벤치마크보다 우수한 성능을 보인다.
• 보고된 실험에서 학습된 수리를 갖춘 단일 인스턴스 NLNS가 최첨단 최적화 방법(UHGS 및 LKH3)의 성능에 근접하거나 일치한다.
• 평가자(critic)를 이용한 강화 학습으로 수리를 학습시키면 학습이 안정되고 더 큰 인스턴스에 일반화되는 확장 가능한 수리가 생성된다.