The min-conflicts heuristic: Experimental and theoretical results

This paper describes a simple heuristic method for solving large-scale constraint satisfaction and scheduling problems. Given an initial assignment for the variables in a problem, the method operates by searching through the space of possible repairs. The search is guided by an ordering heuristic, the min-conflicts heuristic, that attempts to minimize the number of constraint violations after each step. We demonstrate empirically that the method performs orders of magnitude better than traditional backtracking techniques on certain standard problems. For example, the one million queens problem can be solved rapidly using our approach. We also describe practical scheduling applications where the method has been successfully applied. A theoretical analysis is presented to explain why the method works so well on certain types of problems and to predict when it is likely to be most effective

A New Method to Solve the Constraint Satisfaction Problem Using the Hopfield Neural Network

The constraint satisfaction problem is constituted by several condition formulas, which makes it difficult to be solved. In this paper, using the Hopfield neural network, a new method is proposed to solve the constraint satisfaction problem by simplifying its condition formula. In this method, all restriction conditions of a constraint satisfaction problem are divided into two restrictions: restriction I and restriction II. In processing step, restriction II is satisfied by setting its value to be 0 and the value of restriction I is always made on the decreasing direction. The optimum solution could be obtained when the values of energy, restriction I and restriction II become 0 at the same time. To verify the validity of the proposed method, we apply it to two typical constraint satisfaction problems: N-queens problem and four-coloring problem. The simulation results show that the optimum solution can be obtained in high speed and high convergence rate. Moreover, compared with other methods, the proposed method is better than other methods. (author abst.

An event-based architecture for solving constraint satisfaction problems

Constraint satisfaction problems (CSPs) are typically solved using conventional von Neumann computing architectures. However, these architectures do not reflect the distributed nature of many of these problems and are thus ill-suited to solving them. In this paper we present a hybrid analog/digital hardware architecture specifically designed to solve such problems. We cast CSPs as networks of stereotyped multi-stable oscillatory elements that communicate using digital pulses, or events. The oscillatory elements are implemented using analog non-stochastic circuits. The non-repeating phase relations among the oscillatory elements drive the exploration of the solution space. We show that this hardware architecture can yield state-of-the-art performance on a number of CSPs under reasonable assumptions on the implementation. We present measurements from a prototype electronic chip to demonstrate that a physical implementation of the proposed architecture is robust to practical non-idealities and to validate the theory proposed.Comment: First two authors contributed equally to this wor

Model Agnostic solution of CSPs with Deep Learning

Negli ultimi anni, le tecniche di Deep Learning sono state notevolmente migliorate, permettendo di affrontare con successo numerosi problemi. Il Deep Learning ha un approccio sub-simbolico ai problemi, perciò non si rende necessario descrivere esplicitamente informazioni sulla struttura del problema per fare sì che questo possa essere affrontato con successo; l'idea è quindi di utilizzare reti neurali di Deep Learning per affrontare problemi con vincoli (CSPs), senza dover fare affidamento su conoscenza esplicita riguardo ai vincoli dei problemi. Chiamiamo questo approccio Model Agnostic; esso può rivelarsi molto utile se usato sui CSP, dal momento che è spesso difficile esprimerne tutti i dettagli: potrebbero esistere vincoli, o preferenze, che non sono menzionati esplicitamente, e che sono intuibili solamente dall'analisi di soluzioni precedenti del problema. In questi casi, un modello di Deep Learning in grado di apprendere la struttura del CSP potrebbe avere applicazioni pratiche rilevanti. In particolar modo, in questa tesi si è indagato sul fatto che una Deep Neural Network possa essere capace di risolvere il rompicapo delle 8 regine. Sono state create due diverse reti neurali, una rete Generatore e una rete Discriminatore, che hanno dovuto apprendere differenti caratteristiche del problema. La rete Generatore è stata addestrata per produrre un singolo assegnamento, in modo che questo sia globalmente consistente; la rete Discriminatore è stata invece addestrata a distinguere tra soluzioni ammissibili e non ammissibili, con l'idea che possa essere utilizzata come controllore dell'euristica. Infine, sono state combinate le due reti in un unico modello, chiamato Generative Adversarial Network (GAN), in modo che esse possano scambiarsi conoscenza riguardo al problema, con l'obiettivo di migliorare le prestazioni di entrambe

Hopfield networks, neural data structures and the nine flies problem: neural network programming projects for undergraduates

This paper describes two neural network programming projects suitable for undergraduate students who have already completed introductory courses in Programming and Data Structures. It briefly outlines the structure and operation of Hopfield Networks from a data structure stand-point and demonstrates how these type of neural networks may be used to solve interesting problems like Perelman's Nine Flies Problem. Although the Hopfield model is well defined mathematically, students do not have to be very familiar with the mathematics of the model in order to use it to solve problems. Students are actively encouraged to design modifications to their implementations in order to obtain faster or more accurate solutions. Additionally, students are also expected to compare the neural network's performance with traditional approaches, in order that they may appreciate the subtleties of both approaches. Sample results are provided from projects which have been completed during the last three-year period

Using deep reinforcement learning to search reachability properties in systems specified through graph transformation

Today, model checking is one of the essential techniques in the verification of software systems. This technique can verify some properties such as reachability in which the entire state space is searched to find the desired state. However, model checking may lead to the state space explosion problem in which all states cannot be generated due to the exponential resource usage. Although the results of recent model checking approaches are promising, there is still room for improvement in terms of accuracy and the number of explored states. In this paper, using deep reinforcement learning and two neural networks, we propose an approach to increase the accuracy of the generated witnesses and reduce the use of hardware resources. In this approach, at first, an agent starts to explore the state space without any knowledge and gradually identifies the proper and improper actions by receiving different rewards/penalties from the environment to achieve the goal. Once the dataset is fulfilled with the agent's experiences, two neural networks evaluate the quality of each operation in each state, and afterwards, the best action is selected. The significant difficulties and challenges in the implementation are encoding the states, feature engineering, feature selection, reward engineering, handling invalid actions, and configuring the neural network. Finally, the proposed approach has been implemented in the Groove toolset, and as a result, in most of the case studies, it overcame the problem of state space explosion. Also, this approach outperforms the existing solutions in terms of generating shorter witnesses and exploring fewer states. On average, the proposed approach is nearly 400% better than other approaches in exploring fewer states and 300% better than the others in generating shorter witnesses. Also, on average, the proposed approach is 37% more accurate than the others in terms of finding the goals state

A Genetic Algorithm Based Approach for Solving the Minimum Dominating Set of Queens Problem

In the field of computing, combinatorics, and related areas, researchers have formulated several techniques for the Minimum Dominating Set of Queens Problem (MDSQP) pertaining to the typical chessboard based puzzles. However, literature shows that limited research has been carried out to solve theMDSQP using bioinspired algorithms. To fill this gap, this paper proposes a simple and effective solution based on genetic algorithms to solve this classical problem. We report results which demonstrate that near optimal solutions have been determined by the GA for different board sizes ranging from 8 × 8 to 11 × 11