This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformu-lations that approximate the Euclidean distances and simplify the objective function. Additionally, the use of convex sets in the constraint design offers computational benefits. The proposed methodology is empirically validated on real-world CETSP instances, with the aid of computational strategies such as a fragmented CPLEX-based approach. Results demonstrate its effectiveness in managing computational resources without compromising solution quality. Furthermore, the article analyzes the behavior of the proposed mathematical formulations, providing comprehensive insights into their performance.

This study aims to address the key challenge of obtaining a high-quality solution path within a short calculation time by generalizing a limited dataset. In the informed experience-driven random trees connect star (IERTC*) process, the algorithm flexibly explores the search trees by morphing the micro paths generated from a single experience while reducing the path cost by introducing a re-wiring process and an informed sampling process. The core idea of this algorithm is to apply different strategies depending on the complexity of the local environment; for example, it adopts a more complex curved trajectory if obstacles are densely arranged near the search tree, and it adopts a simpler straight line if the local environment is sparse. The results of experiments using a general motion benchmark test revealed that IERTC* significantly improved the planning success rate in difficult problems in the cluttered environment (an average improvement of 49.3% compared to the state-of-the-art algorithm) while also significantly reducing the solution cost (a reduction of 56.3%) when using one hundred experiences. Furthermore, the results demonstrated outstanding planning performance even when only one experience was available (a 43.8% improvement in success rate and a 57.8% reduction in solution cost).

In earthwork and construction, excavators often encounter large rocks mixed with various soil conditions, requiring skilled operators. This paper presents a framework for achieving autonomous excavation using reinforcement learning (RL) through a rock excavation simulator. In the simulation, resolution can be defined by the particle size/number in the whole soil space. Fine-resolution simulations closely mimic real-world behavior but demand significant calculation time and challenging sample collection, while coarse-resolution simulations enable faster sample collection but deviate from real-world behavior. To combine the advantages of both resolutions, we explore using policies developed in coarse-resolution simulations for pre-training in fine-resolution simulations. To this end, we propose a novel policy learning framework called Progressive-Resolution Policy Distillation (PRPD), which progressively transfers policies through some middle-resolution simulations with conservative policy transfer to avoid domain gaps that could lead to policy transfer failure. Validation in a rock excavation simulator and nine real-world rock environments demonstrated that PRPD reduced sampling time to less than 1/7 while maintaining task success rates comparable to those achieved through policy learning in a fine-resolution simulation.

Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. It extends principal component analysis (PCA) and can extract important and complicated components with small variances. One of the major problems of ICA is that the uniqueness of the solution is not guaranteed, unlike PCA. That is because there are many local optima in optimizing the objective function of ICA. It has been shown previously that the unique global optimum of ICA can be estimated from many random initializations by handcrafted thread computation. In this paper, the unique estimation of ICA is highly accelerated by reformulating the algorithm in matrix representation and reducing redundant calculations. Experimental results on artificial datasets and EEG data verified the efficiency of the proposed method.

This paper aims to answer the question: Can deep learning models be cost-efficiently trained on a global market of spot VMs spanning different data centers and cloud providers? To provide guidance, we extensively evaluate the cost and throughput implications of training in different zones, continents, and clouds for representative CV, NLP, and ASR models. To expand the current training options further, we compare the scalability potential for hybrid-cloud scenarios by adding cloud resources to on-premise hardware to improve training throughput. Finally, we show how leveraging spot instance pricing enables a new cost-efficient way to train models with multiple cheap VMs, trumping both more centralized and powerful hardware and even on-demand cloud offerings at competitive prices.

Multi-goal path finding (MGPF) aims to find a closed and collision-free path to visit a sequence of goals orderly. As a physical travelling salesman problem, an undirected complete graph with accurate weights is crucial for determining the visiting order. Lack of prior knowledge of local paths between vertices poses challenges in meeting the optimality and efficiency requirements of algorithms. In this study, a multi-task learning model designated Prior Knowledge Extraction (PKE), is designed to estimate the local path length between pairwise vertices as the weights of the graph. Simultaneously, a promising region and a guideline are predicted as heuristics for the path-finding process. Utilizing the outputs of the PKE model, a variant of Rapidly-exploring Random Tree (RRT) is proposed known as PKE-RRT. It effectively tackles the MGPF problem by a local planner incorporating a prioritized visiting order, which is obtained from the complete graph. Furthermore, the predicted region and guideline facilitate efficient exploration of the tree structure, enabling the algorithm to rapidly provide a sub-optimal solution. Extensive numerical experiments demonstrate the outstanding performance of the PKE-RRT for the MGPF problem with a different number of goals, in terms of calculation time, path cost, sample number, and success rate.

After the discovery of Shor's algorithm and Grover's search algorithm, there has been many researches covering the concept of quantum advantage, which insists quantum computers will exhibit specific advantages over classical computers. Google named the advantage as "Quantum Supremacy"[1] and explains for specific problems, quantum computers can surpass classical computer in computation time and required memory capacity. However, complex quantum algorithms such as Shor's algorithm requires number of qubits and gate fidelity exponentially more than currently we have, and therefore investigating executable algorithms that show quantum advantage even with noisy and few qubits have been arised as an important question in the NISQ (Noisy Intermediate-Scale Quantum) era[2]. Among them, VQAs (Variational Quantum Algorithms)[3] have been remarked as efficient algorithms that can been executed in NISQ devices with low limitation. VQA is a hybrid quantum algorithm that utilizes classical optimizer and Variational Quantum Circuit (VQC), it first measures a state's probability after quantum circuit, and passes the result to classical optimizer.

In this article an innovative method for training regressive MLP networks is presented, which is not subject to local minima. The Error-Back-Propagation algorithm, proposed by William-Hinton-Rummelhart, has had the merit of favouring the development of machine learning techniques, which has permeated every branch of research and technology since the mid-1980s. This extraordinary success is largely due to the black-box approach, but this same factor was also seen as a limitation, as soon more challenging problems were approached. One of the most critical aspects of the training algorithms was that of local minima of the loss function, typically the mean squared error of the output on the training set. In fact, as the most popular training algorithms are driven by the derivatives of the loss function, there is no possibility to evaluate if a reached minimum is local or global. The algorithm presented in this paper avoids the problem of local minima, as the training is based on the properties of the distribution of the training set, or better on its image internal to the neural network. The performance of the algorithm is shown for a well-known benchmark.

Sampling-based path planning algorithms suffer from heavy reliance on uniform sampling, which accounts for unreliable and time-consuming performance, especially in complex environments. Recently, neural-network-driven methods predict regions as sampling domains to realize a non-uniform sampling and reduce calculation time. However, the accuracy of region prediction hinders further improvement. We propose a sampling-based algorithm, abbreviated to Region Prediction Neural Network RRT* (RPNN-RRT*), to rapidly obtain the optimal path based on a high-accuracy region prediction. First, we implement a region prediction neural network (RPNN), to predict accurate regions for the RPNN-RRT*. A full-layer channel-wise attention module is employed to enhance the feature fusion in the concatenation between the encoder and decoder. Moreover, a three-level hierarchy loss is designed to learn the pixel-wise, map-wise, and patch-wise features. A dataset, named Complex Environment Motion Planning, is established to test the performance in complex environments. Ablation studies and test results show that a high accuracy of 89.13% is achieved by the RPNN for region prediction, compared with other region prediction models. In addition, the RPNN-RRT* performs in different complex scenarios, demonstrating significant and reliable superiority in terms of the calculation time, sampling efficiency, and success rate for optimal path planning.

In this paper, we propose a novel end-to-end approach for solving the multi-goal path planning problem in obstacle environments. Our proposed model, called S&Reg, integrates multi-task learning networks with a TSP solver and a path planner to quickly compute a closed and feasible path visiting all goals. Specifically, the model first predicts promising regions that potentially contain the optimal paths connecting two goals as a segmentation task. Simultaneously, estimations for pairwise distances between goals are conducted as a regression task by the neural networks, while the results construct a symmetric weight matrix for the TSP solver. Leveraging the TSP result, the path planner efficiently explores feasible paths guided by promising regions. We extensively evaluate the S&Reg model through simulations and compare it with the other sampling-based algorithms. The results demonstrate that our proposed model achieves superior performance in respect of computation time and solution cost, making it an effective solution for multi-goal path planning in obstacle environments. The proposed approach has the potential to be extended to other sampling-based algorithms for multi-goal path planning.