skip to main content


Title: A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack
Abstract

In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches.

 
more » « less
NSF-PAR ID:
10491027
Author(s) / Creator(s):
;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Journal of Global Optimization
ISSN:
0925-5001
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We consider the problem of spectrum sharing by multiple cellular operators. We propose a novel deep Reinforcement Learning (DRL)-based distributed power allocation scheme which utilizes the multi-agent Deep Deterministic Policy Gradient (MA-DDPG) algorithm. In particular, we model the base stations (BSs) that belong to the multiple operators sharing the same band, as DRL agents that simultaneously determine the transmit powers to their scheduled user equipment (UE) in a synchronized manner. The power decision of each BS is based on its own observation of the radio environment (RF) environment, which consists of interference measurements reported from the UEs it serves, and a limited amount of information obtained from other BSs. One advantage of the proposed scheme is that it addresses the single-agent non-stationarity problem of RL in the multi-agent scenario by incorporating the actions and observations of other BSs into each BS's own critic which helps it to gain a more accurate perception of the overall RF environment. A centralized-training-distributed-execution framework is used to train the policies where the critics are trained over the joint actions and observations of all BSs while the actor of each BS only takes the local observation as input in order to produce the transmit power. Simulation with the 6 GHz Unlicensed National Information Infrastructure (U-NII)-5 band shows that the proposed power allocation scheme can achieve better throughput performance than several state-of-the-art approaches. 
    more » « less
  2. Purpose Marine transportation has been faced with an increasing demand for containerized cargo during the past decade. Marine container terminals (MCTs), as the facilities for connecting seaborne and inland transportation, are expected to handle the increasing amount of containers, delivered by vessels. Berth scheduling plays an important role for the total throughput of MCTs as well as the overall effectiveness of the MCT operations. This study aims to propose a novel island-based metaheuristic algorithm to solve the berth scheduling problem and minimize the total cost of serving the arriving vessels at the MCT. Design/methodology/approach A universal island-based metaheuristic algorithm (UIMA) was proposed in this study, aiming to solve the spatially constrained berth scheduling problem. The UIMA population was divided into four sub-populations (i.e. islands). Unlike the canonical island-based algorithms that execute the same metaheuristic on each island, four different population-based metaheuristics are adopted within the developed algorithm to search the islands, including the following: evolutionary algorithm (EA), particle swarm optimization (PSO), estimation of distribution algorithm (EDA) and differential evolution (DE). The adopted population-based metaheuristic algorithms rely on different operators, which facilitate the search process for superior solutions on the UIMA islands. Findings The conducted numerical experiments demonstrated that the developed UIMA algorithm returned near-optimal solutions for the small-size problem instances. As for the large-size problem instances, UIMA was found to be superior to the EA, PSO, EDA and DE algorithms, which were executed in isolation, in terms of the obtained objective function values at termination. Furthermore, the developed UIMA algorithm outperformed various single-solution-based metaheuristic algorithms (including variable neighborhood search, tabu search and simulated annealing) in terms of the solution quality. The maximum UIMA computational time did not exceed 306 s. Research limitations/implications Some of the previous berth scheduling studies modeled uncertain vessel arrival times and/or handling times, while this study assumed the vessel arrival and handling times to be deterministic. Practical implications The developed UIMA algorithm can be used by the MCT operators as an efficient decision support tool and assist with a cost-effective design of berth schedules within an acceptable computational time. Originality/value A novel island-based metaheuristic algorithm is designed to solve the spatially constrained berth scheduling problem. The proposed island-based algorithm adopts several types of metaheuristic algorithms to cover different areas of the search space. The considered metaheuristic algorithms rely on different operators. Such feature is expected to facilitate the search process for superior solutions. 
    more » « less
  3. To make daily decisions, human agents devise their own "strategies" governing their mobility dynamics (e.g., taxi drivers have preferred working regions and times, and urban commuters have preferred routes and transit modes). Recent research such as generative adversarial imitation learning (GAIL) demonstrates successes in learning human decision-making strategies from their behavior data using deep neural networks (DNNs), which can accurately mimic how humans behave in various scenarios, e.g., playing video games, etc. However, such DNN-based models are "black box" models in nature, making it hard to explain what knowledge the models have learned from human, and how the models make such decisions, which was not addressed in the literature of imitation learning. This paper addresses this research gap by proposing xGAIL, the first explainable generative adversarial imitation learning framework. The proposed xGAIL framework consists of two novel components, including Spatial Activation Maximization (SpatialAM) and Spatial Randomized Input Sampling Explanation (SpatialRISE), to extract both global and local knowledge from a well-trained GAIL model that explains how a human agent makes decisions. Especially, we take taxi drivers' passenger-seeking strategy as an example to validate the effectiveness of the proposed xGAIL framework. Our analysis on a large-scale real-world taxi trajectory data shows promising results from two aspects: i) global explainable knowledge of what nearby traffic condition impels a taxi driver to choose a particular direction to find the next passenger, and ii) local explainable knowledge of what key (sometimes hidden) factors a taxi driver considers when making a particular decision. 
    more » « less
  4. Andrei Ciortea ; Mehdi Dastani ; Jieting Luo (Ed.)
    The Multi-Agent Path Finding (MAPF) is a problem of finding a plan for agents to reach their desired locations without colliding. Distributed Multi-Agent Path Finder (DMAPF) solves the MAPF problem by decomposing a given MAPF problem instance into smaller subproblems and solve them in parallel. DMAPF works in rounds. Between two consecutive rounds, agents may migrate between two adjacent subproblems following their abstract plans, which are pre-computed, until all of them reach the areas that contain their desired locations. Previous works on DMAPF compute an abstract plan for each agent without the knowledge of other agents’ abstract plans, resulting in high congestion in some areas, especially those that act as corridors. The congestion negatively impacts the runtime of DMAPF and prevents it from being able to solve dense MAPF problems. In this paper, we (i) investigate the use of Uniform-Cost Search to mitigate the congestion. Additionally, we explore the use of several other techniques including (ii) using timeout estimation to preemptively stop solving and relax a subproblem when it is likely to get stuck; (iii) allowing a solving process to manage multiple subproblems – aimed to increase concurrency; and (iv) integrating with MAPF solvers from the Conflict-Based Search family. Experimental results show that our new system is several times faster than the previous ones; can solve larger and denser problems that were unsolvable before; and has better runtime than PBS and EECBS, which are state-of-the-art centralized suboptimal MAPF solvers, in problems with a large number of agents. 
    more » « less
  5. Obeid, I. ; Selesnik, I. ; Picone, J. (Ed.)
    The Neuronix high-performance computing cluster allows us to conduct extensive machine learning experiments on big data [1]. This heterogeneous cluster uses innovative scheduling technology, Slurm [2], that manages a network of CPUs and graphics processing units (GPUs). The GPU farm consists of a variety of processors ranging from low-end consumer grade devices such as the Nvidia GTX 970 to higher-end devices such as the GeForce RTX 2080. These GPUs are essential to our research since they allow extremely compute-intensive deep learning tasks to be executed on massive data resources such as the TUH EEG Corpus [2]. We use TensorFlow [3] as the core machine learning library for our deep learning systems, and routinely employ multiple GPUs to accelerate the training process. Reproducible results are essential to machine learning research. Reproducibility in this context means the ability to replicate an existing experiment – performance metrics such as error rates should be identical and floating-point calculations should match closely. Three examples of ways we typically expect an experiment to be replicable are: (1) The same job run on the same processor should produce the same results each time it is run. (2) A job run on a CPU and GPU should produce identical results. (3) A job should produce comparable results if the data is presented in a different order. System optimization requires an ability to directly compare error rates for algorithms evaluated under comparable operating conditions. However, it is a difficult task to exactly reproduce the results for large, complex deep learning systems that often require more than a trillion calculations per experiment [5]. This is a fairly well-known issue and one we will explore in this poster. Researchers must be able to replicate results on a specific data set to establish the integrity of an implementation. They can then use that implementation as a baseline for comparison purposes. A lack of reproducibility makes it very difficult to debug algorithms and validate changes to the system. Equally important, since many results in deep learning research are dependent on the order in which the system is exposed to the data, the specific processors used, and even the order in which those processors are accessed, it becomes a challenging problem to compare two algorithms since each system must be individually optimized for a specific data set or processor. This is extremely time-consuming for algorithm research in which a single run often taxes a computing environment to its limits. Well-known techniques such as cross-validation [5,6] can be used to mitigate these effects, but this is also computationally expensive. These issues are further compounded by the fact that most deep learning algorithms are susceptible to the way computational noise propagates through the system. GPUs are particularly notorious for this because, in a clustered environment, it becomes more difficult to control which processors are used at various points in time. Another equally frustrating issue is that upgrades to the deep learning package, such as the transition from TensorFlow v1.9 to v1.13, can also result in large fluctuations in error rates when re-running the same experiment. Since TensorFlow is constantly updating functions to support GPU use, maintaining an historical archive of experimental results that can be used to calibrate algorithm research is quite a challenge. This makes it very difficult to optimize the system or select the best configurations. The overall impact of all of these issues described above is significant as error rates can fluctuate by as much as 25% due to these types of computational issues. Cross-validation is one technique used to mitigate this, but that is expensive since you need to do multiple runs over the data, which further taxes a computing infrastructure already running at max capacity. GPUs are preferred when training a large network since these systems train at least two orders of magnitude faster than CPUs [7]. Large-scale experiments are simply not feasible without using GPUs. However, there is a tradeoff to gain this performance. Since all our GPUs use the NVIDIA CUDA® Deep Neural Network library (cuDNN) [8], a GPU-accelerated library of primitives for deep neural networks, it adds an element of randomness into the experiment. When a GPU is used to train a network in TensorFlow, it automatically searches for a cuDNN implementation. NVIDIA’s cuDNN implementation provides algorithms that increase the performance and help the model train quicker, but they are non-deterministic algorithms [9,10]. Since our networks have many complex layers, there is no easy way to avoid this randomness. Instead of comparing each epoch, we compare the average performance of the experiment because it gives us a hint of how our model is performing per experiment, and if the changes we make are efficient. In this poster, we will discuss a variety of issues related to reproducibility and introduce ways we mitigate these effects. For example, TensorFlow uses a random number generator (RNG) which is not seeded by default. TensorFlow determines the initialization point and how certain functions execute using the RNG. The solution for this is seeding all the necessary components before training the model. This forces TensorFlow to use the same initialization point and sets how certain layers work (e.g., dropout layers). However, seeding all the RNGs will not guarantee a controlled experiment. Other variables can affect the outcome of the experiment such as training using GPUs, allowing multi-threading on CPUs, using certain layers, etc. To mitigate our problems with reproducibility, we first make sure that the data is processed in the same order during training. Therefore, we save the data from the last experiment and to make sure the newer experiment follows the same order. If we allow the data to be shuffled, it can affect the performance due to how the model was exposed to the data. We also specify the float data type to be 32-bit since Python defaults to 64-bit. We try to avoid using 64-bit precision because the numbers produced by a GPU can vary significantly depending on the GPU architecture [11-13]. Controlling precision somewhat reduces differences due to computational noise even though technically it increases the amount of computational noise. We are currently developing more advanced techniques for preserving the efficiency of our training process while also maintaining the ability to reproduce models. In our poster presentation we will demonstrate these issues using some novel visualization tools, present several examples of the extent to which these issues influence research results on electroencephalography (EEG) and digital pathology experiments and introduce new ways to manage such computational issues. 
    more » « less