234 research outputs found

    Sequential and parallel large neighborhood search algorithms for the periodic location routing problem

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    We propose a large neighborhood search (LNS) algorithm to solve the periodic location routing problem (PLRP). The PLRP combines location and routing decisions over a planning horizon in which customers require visits according to a given frequency and the specific visit days can be chosen. We use parallelization strategies that can exploit the availability of multiple processors. The computational results show that the algorithms obtain better results than previous solution methods on a set of standard benchmark instances from the literature

    Adaptive large neighborhood search algorithm – performance evaluation under parallel schemes & applications

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    Adaptive Large Neighborhood Search (ALNS) is a fairly recent yet popular single-solution heuristic for solving discrete optimization problems. Even though the heuristic has been a popular choice for researchers in recent times, the parallelization of this algorithm is not widely studied in the literature compared to the other classical metaheuristics. To extend the existing literature, this study proposes several different parallel schemes to parallelize the basic/sequential ALNS algorithm. More specifically, seven different parallel schemes are employed to target different characteristics of the ALNS algorithm and the capability of the local computers. The schemes of this study are implemented in a master-slave architecture to manage and assign loads in processors of the local computers. The overall goal is to simultaneously explore different areas of the search space in an attempt to escape the local minima, taking effective steps toward the optimal solution and, to the end, accelerating the convergence of the ALNS algorithm. The performance of the schemes is tested by solving a capacitated vehicle routing problem (CVRP) with available wellknown test instances. Our computational results indicate that all the parallel schemes are capable of providing a competitive optimality gap in solving CVRP within our investigated test instances. However, the parallel scheme (scheme 1), which runs the ALNS algorithm independently within different slave processors (e.g., without sharing any information with other slave processors) until the synchronization occurs only when one of the processors meets its predefined termination criteria and reports the solution to the master processor, provides the best running time with solving the instances approximately 10.5 times faster than the basic/sequential ALNS algorithm. These findings are applied in a real-life fulfillment process using mixed-mode delivery with trucks and drones. Complex but optimized routes are generated in a short time that is applicable to perform last-mile delivery to customers

    Attention, Learn to Solve Routing Problems!

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    The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.Comment: Accepted at ICLR 2019. 25 pages, 7 figure

    Routing Arena: A Benchmark Suite for Neural Routing Solvers

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    Neural Combinatorial Optimization has been researched actively in the last eight years. Even though many of the proposed Machine Learning based approaches are compared on the same datasets, the evaluation protocol exhibits essential flaws and the selection of baselines often neglects State-of-the-Art Operations Research approaches. To improve on both of these shortcomings, we propose the Routing Arena, a benchmark suite for Routing Problems that provides a seamless integration of consistent evaluation and the provision of baselines and benchmarks prevalent in the Machine Learning- and Operations Research field. The proposed evaluation protocol considers the two most important evaluation cases for different applications: First, the solution quality for an a priori fixed time budget and secondly the anytime performance of the respective methods. By setting the solution trajectory in perspective to a Best Known Solution and a Base Solver's solutions trajectory, we furthermore propose the Weighted Relative Average Performance (WRAP), a novel evaluation metric that quantifies the often claimed runtime efficiency of Neural Routing Solvers. A comprehensive first experimental evaluation demonstrates that the most recent Operations Research solvers generate state-of-the-art results in terms of solution quality and runtime efficiency when it comes to the vehicle routing problem. Nevertheless, some findings highlight the advantages of neural approaches and motivate a shift in how neural solvers should be conceptualized

    Combining Constructive and Perturbative Deep Learning Algorithms for the Capacitated Vehicle Routing Problem

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    The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive and perturbative heuristics to tackle this problem using Deep Learning. In this paper, we join these efforts to develop the Combined Deep Constructor and Perturbator, which combines two powerful constructive and perturbative Deep Learning-based heuristics, using attention mechanisms at their core. Furthermore, we improve the Attention Model-Dynamic for the Capacitated Vehicle Routing Problem by proposing a memory-efficient algorithm that reduces its memory complexity by a factor of the number of nodes. Our method shows promising results. It demonstrates a cost improvement in common datasets when compared against other multiple Deep Learning methods. It also obtains close results to the state-of-the art heuristics from the Operations Research field. Additionally, the proposed memory efficient algorithm for the Attention Model-Dynamic model enables its use in problem instances with more than 100 nodes
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