Neural architecture search (NAS) is a challenging problem. Hierarchical search spaces allow for cheap evaluations of neural network sub modules to serve as surrogate for architecture evaluations. Yet, sometimes the hierarchy is too restrictive or the surrogate fails to generalize. We present FaDE which uses differentiable architecture search to obtain relative performance predictions on finite regions of a hierarchical NAS space. The relative nature of these ranks calls for a memory-less, batch-wise outer search algorithm for which we use an evolutionary algorithm with pseudo-gradient descent. FaDE is especially suited on deep hierarchical, respectively multi-cell search spaces, which it can explore by linear instead of exponential cost and therefore eliminates the need for a proxy search space. Our experiments show that firstly, FaDE-ranks on finite regions of the search space correlate with corresponding architecture performances and secondly, the ranks can empower a pseudo-gradient evolutionary search on the complete neural architecture search space.

In this paper, we propose a quantum computing oriented benchmark for combinatorial optimization. This benchmark, coined as QOPTLib, is composed of 40 instances equally distributed over four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem and the Maximum Cut Problem. The sizes of the instances in QOPTLib not only correspond to computationally addressable sizes, but also to the maximum length approachable with non-zero likelihood of getting a good result. In this regard, it is important to highlight that hybrid approaches are also taken into consideration. Thus, this benchmark constitutes the first effort to provide users a general-purpose dataset. Also in this paper, we introduce a first full solving of QOPTLib using two solvers based on quantum annealing. Our main intention with this is to establish a preliminary baseline, hoping to inspire other researchers to beat these outcomes with newly proposed quantum-based algorithms.

The shift from Cloud Computing to a Cloud-Edge continuum presents new opportunities and challenges for data-intensive and interactive applications. Edge computing has garnered a lot of attention from both industry and academia in recent years, emerging as a key enabler for meeting the increasingly strict demands of Next Generation applications. In Edge computing the computations are placed closer to the end-users, to facilitate low-latency and high-bandwidth applications and services. However, the distributed, dynamic, and heterogeneous nature of Edge computing, presents a significant challenge for service placement. A critical aspect of Edge computing involves managing the placement of applications within the network system to minimize each application's runtime, considering the resources available on system devices and the capabilities of the system's network. The placement of application images must be proactively planned to minimize image tranfer time, and meet the strict demands of the applications. In this regard, this paper proposes an approach for proactive image placement that combines Graph Neural Networks and actor-critic Reinforcement Learning, which is evaluated empirically and compared against various solutions. The findings indicate that although the proposed approach may result in longer execution times in certain scenarios, it consistently achieves superior outcomes in terms of application placement.

In the domain of artificial intelligence, two-player board games have historically served as pivotal'toy problems' for exploring and advancing search and planning algorithms within vast decision spaces. The outstanding algorithm AlphaZero (Silver et al. [2016] Silver et al. [2017a] Silver et al. [2017b]) achieved superhuman performance in the game of Go, chess, and other board games without the use of human expertise in these games. In this work, we introduce a new approach to solving such games. The main idea is that the algorithm iterates through possible moves using beam search, and then learns to predict the outcome of this search. This concept gives rise to the name of the algorithm, PROBS - Predict Results of Beam Search. This approach shows promising results -- it demonstrates an increase in the winning percentage during the training process and shows improvement with the use of greater computational power. Although this new approach to solving board games does not improve upon state-of-the-art approaches, it demonstrates a new working concept that may inspire researchers to develop new methods in other areas. The foundation of the PROBS algorithm is the iterative training of two neural networks. The first network is a value function, V (s), which predicts the expected utility from the current state.

Grover's search algorithms, including various partial Grover searches, experience scaling problems as the number of iterations rises with increased qubits, making implementation more computationally expensive. This paper combines Partial Grover's search algorithm and Bi-directional Search to create a fast Grover's quantum search algorithm, referred to as Bi-Directional Grover Search (BDGS). We incorporated a bi-directional search tactic with a partial Grover search, starting from an initial state and a single marked state in parallel. We have shown in this article that our novel approach requires $\frac{\pi}{4\sqrt{2}}\sqrt{N}(1-\sqrt{\frac{1}{b^{r/2k}}})$ iterations over regular Grover Search and Partial Grover Search (PGS), which takes $\frac{\pi}{4}\sqrt{N}\sqrt{1-\frac{1}{b}}$ (here, $N=2^r$ elements, $b$ is the branching factor of partial search, and $k= \lceil\log_2b \rceil$). The proposed BDGS algorithm is benchmarked against the state-of-the-art Depth-First Grover's Search (DFGS) and generic Grover's Search (GS) implementations for $2$ to $20$ qubits and provides promising results. The Qiskit Python implementation of the proposed BDGS algorithm is available on Github (https://github.com/hafeezzwiz21/DFGS-BDGS).

Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates additional columns as needed. However, the generation of columns often requires solving difficult subproblems repeatedly, which can be a bottleneck for CG. To address this challenge, we propose a novel method called machine learning enhanced ant colony optimization (MLACO), to efficiently generate multiple high-quality columns from a subproblem. Specifically, we train a ML model to predict the optimal solution of a subproblem, and then integrate this ML prediction into the probabilistic model of ACO to sample multiple high-quality columns. Our experimental results on the bin packing problem with conflicts show that the MLACO method significantly improves the performance of CG compared to several state-of-the-art methods. Furthermore, when our method is incorporated into a Branch-and-Price method, it leads to a significant reduction in solution time.

Geometric problem solving has always been a long-standing challenge in the fields of automated reasoning and artificial intelligence. We built a neural-symbolic system to automatically perform human-like geometric deductive reasoning. The symbolic part is a formal system built on FormalGeo, which can automatically perform geomertic relational reasoning and algebraic calculations and organize the solving process into a solution hypertree with conditions as hypernodes and theorems as hyperedges. The neural part, called HyperGNet, is a hypergraph neural network based on the attention mechanism, including a encoder to effectively encode the structural and semantic information of the hypertree, and a solver to provide problem-solving guidance. The neural part predicts theorems according to the hypertree, and the symbolic part applies theorems and updates the hypertree, thus forming a predict-apply cycle to ultimately achieve readable and traceable automatic solving of geometric problems. Experiments demonstrate the correctness and effectiveness of this neural-symbolic architecture. We achieved a step-wised accuracy of 87.65% and an overall accuracy of 85.53% on the formalgeo7k datasets.

Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as heat diffusion can solve the graph coloring problem. We propose a solution to the graph coloring problem using the heat diffusion framework. We compare the solutions against popular methods and establish the competitiveness of heat diffusion method for the graph coloring problem.

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module -- that formulates the cut selection as a sequence/set to sequence learning problem -- to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

Traditional search algorithms have issues when applied to games of imperfect information where the number of possible underlying states and trajectories are very large. This challenge is particularly evident in trick-taking card games. While state sampling techniques such as Perfect Information Monte Carlo (PIMC) search has shown success in these contexts, they still have major limitations. We present Generative Observation Monte Carlo Tree Search (GO-MCTS), which utilizes MCTS on observation sequences generated by a game specific model. This method performs the search within the observation space and advances the search using a model that depends solely on the agent's observations. Additionally, we demonstrate that transformers are well-suited as the generative model in this context, and we demonstrate a process for iteratively training the transformer via population-based self-play. The efficacy of GO-MCTS is demonstrated in various games of imperfect information, such as Hearts, Skat, and "The Crew: The Quest for Planet Nine," with promising results.