Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

Deep Policy Dynamic Programming for Vehicle Routing Problems

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other 'neural approaches' for solving TSPs, VRPs and TSPTWs with 100 nodes.Comment: 21 page

From Parameter Tuning to Dynamic Heuristic Selection

The importance of balance between exploration and exploitation plays a crucial role while solving combinatorial optimization problems. This balance is reached by two general techniques: by using an appropriate problem solver and by setting its proper parameters. Both problems were widely studied in the past and the research process continues up until now. The latest studies in the field of automated machine learning propose merging both problems, solving them at design time, and later strengthening the results at runtime. To the best of our knowledge, the generalized approach for solving the parameter setting problem in heuristic solvers has not yet been proposed. Therefore, the concept of merging heuristic selection and parameter control have not been introduced. In this thesis, we propose an approach for generic parameter control in meta-heuristics by means of reinforcement learning (RL). Making a step further, we suggest a technique for merging the heuristic selection and parameter control problems and solving them at runtime using RL-based hyper-heuristic. The evaluation of the proposed parameter control technique on a symmetric traveling salesman problem (TSP) revealed its applicability by reaching the performance of tuned in online and used in isolation underlying meta-heuristic. Our approach provides the results on par with the best underlying heuristics with tuned parameters.:1 Introduction 1 1.1 Motivation 1 1.2 Research objective 2 1.3 Solution overview 2 2 Background and RelatedWork Analysis 3 2.1 Optimization Problems and their Solvers 3 2.2 Heuristic Solvers for Optimization Problems 9 2.3 Setting Algorithm Parameters 19 2.4 Combined Algorithm Selection and Hyper-Parameter Tuning Problem 27 2.5 Conclusion on Background and Related Work Analysis 28 3 Online Selection Hyper-Heuristic with Generic Parameter Control 31 3.1 Combined Parameter Control and Algorithm Selection Problem 31 3.2 Search Space Structure 32 3.3 Parameter Prediction Process 34 3.4 Low-Level Heuristics 35 3.5 Conclusion of Concept 36 4 Implementation Details 37 4.2 Search Space 40 4.3 Prediction Process 43 4.4 Low Level Heuristics 48 4.5 Conclusion 52 5 Evaluation 55 5.1 Optimization Problem 55 5.2 Environment Setup 56 5.3 Meta-heuristics Tuning 56 5.4 Concept Evaluation 60 5.5 Analysis of HH-PC Settings 74 5.6 Conclusion 79 6 Conclusion 81 7 FutureWork 83 7.1 Prediction Process 83 7.2 Search Space 84 7.3 Evaluations and Benchmarks 84 Bibliography 87 A Evaluation Results 99 A.1 Results in Figures 99 A.2 Results in numbers 10