Are you interested in furthering your knowledge of algorithms? Do you want to learn how they work for real-world problems? Then you've come to the right place. This guide will walk you through algorithm design before digging into some of the top design techniques. Here's what you will learn: • The steps involved in designing an algorithm • The top algorithm design techniques • The Divide and Conquer algorithm • The Greedy Algorithm • Dynamic Programming • The Branch and Bound Algorithm • The Randomized Algorithm • Recursion and backtracking And everything that goes with them.

Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination -- a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose an attention encoder-LSTM decoder hybrid model, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for coordinated routing of multiple vehicles than the attention-based model.

Below are three alternatives to Kaggle which I've become interested in: A fourth competition does exist -- HALITE by Two Sigma-- however, HALITE appears to have been discontinued…you're welcome to check it out on your own; only Battlecode, Terminal, and Lux are summarized below. Battle Code has been around since 2003; the description below is taken directly from the site. Battlecode is a real-time strategy game, for which you will write an AI player. Your AI player will need to strategically manage a robot army and control how your robots work together to defeat the enemy team. As a contestant, you will learn to use artificial intelligence, pathfinding, distributed algorithms, and communications to make your player as competitive as possible.

In this paper we present an extension of the Nested Rollout Policy Adaptation algorithm (NRPA), namely the Generalized Nested Rollout Policy Adaptation (GNRPA), as well as its use for solving some instances of the Vehicle Routing Problem. We detail some results obtained on the Solomon instances set which is a conventional benchmark for the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). We show that on all instances, GN-RPA performs better than NRPA. On some instances, it performs better than the Google OR Tool module dedicated to VRP.

It is worth noting that many challenging task not only in its inherent CO problems can be essentially formulated as a graph problem complexity (e.g. NP-hard) but also the possible (Khalil et al., 2017; Bengio et al., 2020), hence it is sensitivity to input conditions. In this paper, we attractive and natural to modify the problem instance by take an initiative on developing the mechanisms modifying the graph structure, to generate more test cases for adversarial attack and defense towards combinatorial for solvers. In fact, vulnerability can often be an inherent optimization solvers, whereby the solver challenge for CO solvers since the problem is often strong is treated as a black-box function and the original nonlinear and NP-hard. From this perspective, we consider problem's underlying graph structure (which is attack and defense CO solvers in the following aspects.

In recent years, Graph Neural Networks (GNNs) have shown superior performance on diverse applications on real-world datasets. To improve the model capacity and alleviate the over-smoothing problem, several methods proposed to incorporate the intermediate layers by layer-wise connections. However, due to the highly diverse graph types, the performance of existing methods vary on diverse graphs, leading to a need for data-specific layer-wise connection methods. To address this problem, we propose a novel framework LLC (Learn Layer-wise Connections) based on neural architecture search (NAS) to learn adaptive connections among intermediate layers in GNNs. LLC contains one novel search space which consists of 3 types of blocks and learnable connections, and one differentiable search algorithm to enable the efficient search process. Extensive experiments on five real-world datasets are conducted, and the results show that the searched layer-wise connections can not only improve the performance but also alleviate the over-smoothing problem.

Hi everyone, today we're going to be comparing Player of Games (PoG) with AlphaZero. PoG is a new AI agent developed by DeepMind and is the first of its kind to achieve high-level performance in both perfect and imperfect information games. With perfect information games, each player knows all the information in the game. For chess and go knowing all the information in the game means players can see both theirs and their opponent's pieces. With imperfect information games, players are unable to see all the information.

Active Directory is the default security management system for Windows domain networks. We study the shortest path edge interdiction problem for defending Active Directory style attack graphs. The problem is formulated as a Stackelberg game between one defender and one attacker. The attack graph contains one destination node and multiple entry nodes. The attacker's entry node is chosen by nature. The defender chooses to block a set of edges limited by his budget. The attacker then picks the shortest unblocked attack path. The defender aims to maximize the expected shortest path length for the attacker, where the expectation is taken over entry nodes. We observe that practical Active Directory attack graphs have small maximum attack path lengths and are structurally close to trees. We first show that even if the maximum attack path length is a constant, the problem is still $W[1]$-hard with respect to the defender's budget. Having a small maximum attack path length and a small budget is not enough to design fixed-parameter algorithms. If we further assume that the number of entry nodes is small, then we derive a fixed-parameter tractable algorithm. We then propose two other fixed-parameter algorithms by exploiting the tree-like features. One is based on tree decomposition and requires a small tree width. The other assumes a small number of splitting nodes (nodes with multiple out-going edges). Finally, the last algorithm is converted into a graph convolutional neural network based heuristic, which scales to larger graphs with more splitting nodes.

Hyperparamter tuning is one of the the most time-consuming parts in machine learning: The performance of a large number of different hyperparameter settings has to be evaluated to find the best one. Although modern optimization algorithms exist that minimize the number of evaluations needed, the evaluation of a single setting is still expensive: Using a resampling technique, the machine learning method has to be fitted a fixed number of $K$ times on different training data sets. As an estimator for the performance of the setting the respective mean value of the $K$ fits is used. Many hyperparameter settings could be discarded after less than $K$ resampling iterations, because they already are clearly inferior to high performing settings. However, in practice, the resampling is often performed until the very end, wasting a lot of computational effort. We propose to use a sequential testing procedure to minimize the number of resampling iterations to detect inferior parameter setting. To do so, we first analyze the distribution of resampling errors, we will find out, that a log-normal distribution is promising. Afterwards, we build a sequential testing procedure assuming this distribution. This sequential test procedure is utilized within a random search algorithm. We compare a standard random search with our enhanced sequential random search in some realistic data situation. It can be shown that the sequential random search is able to find comparably good hyperparameter settings, however, the computational time needed to find those settings is roughly halved.

The 2021 NeurIPS Machine Learning for Combinatorial Optimization (ML4CO) competition was designed with the goal of improving state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning models. The competition's main scientific question was the following: is machine learning a viable option for improving traditional combinatorial optimization solvers on specific problem distributions, when historical data is available? This was motivated by the fact that in many practical scenarios, the data changes only slightly between the repetitions of a combinatorial optimization problem, and this is an area where machine learning models are particularly powerful at. This paper summarizes the solution and lessons learned by the Huawei EI-OROAS team in the dual task of the competition. The submission of our team achieved the second place in the final ranking, with a very close distance to the first spot. In addition, our solution was ranked first consistently for several weekly leaderboard updates before the final evaluation. We provide insights gained from a large number of experiments, and argue that a simple Graph Convolutional Neural Network (GCNNs) can achieve state-of-the-art results if trained and tuned properly.