scholarly journals Global constraints in modeling and solving problems within the Constraint Programming paradigm.

2020 ◽  
Vol 11 (8-2020) ◽  
pp. 67-83
Author(s):  
Yu.A. Oleynik ◽  
◽  
A.A. Zuenko ◽  
Keyword(s):  
Constraint Programming ◽  
High Performance ◽  
Optimization Problems ◽  
Building Blocks ◽  
Global Constraints ◽  
Combinatorial Search ◽  
Combinatorial Optimization Problems ◽  
Programming Paradigm ◽  
Moment Constraint ◽  
The Moment

At the moment, constraint programming technology is a powerful tool for solving combinatorial search and combinatorial optimization problems. To use this technology, any task must be formulated as a task of satisfying constraints. The role of the concept of global constraints in modeling and solving applied problems within the framework of the constraint programming paradigm can hardly be overestimated. The procedures that implement the algorithms of filtering global constraints are the elementary “building blocks” from which the model of a specific applied problem is built. Algorithms for filtering global constraints, as a rule, are supported by the corresponding developed theories that allow organizing high-performance computing. The choice of a particular software library is primarily determined by the extent to which the set and method of implementing global constraints corresponds tothe level of modern research in this area. The main focus of this article is focused on an overview of global constraints that are implemented within the most popular constraint programming libraries: Choco, GeCode, JaCoP, MiniZinc.

scholarly journals Planning of the open-pit working edge positions by the periods of mining within the constraint programming paradigm

2021 ◽  
Vol 12 (5-2021) ◽  
pp. 161-165
Author(s):  
Alexander A. Zuenko ◽  
◽  
Yurii A. Oleynik ◽  
Roman A. Makedonov ◽  
◽  
...  
Keyword(s):  
Constraint Programming ◽  
A Priori ◽  
Three Dimensional ◽  
Open Pit ◽  
Global Constraints ◽  
Combinatorial Search ◽  
Dimensional Problem ◽  
Initial Value ◽  
Programming Paradigm ◽  
Technological Constraints

The work is aimed at solving the three-dimensional problem of finding the open-pit working edge positions by the periods of mining, taking into account the a priori specified productivity for the mineral and overburden. The proposed method uses a block model of a pit, where for each block its coordinates, the content of minerals in it, and the conditional initial value of the block are known. Also, a discounting function is set - a change in the total value of a block, depending on the period of its mining. The task is to find the distribution of blocks over mining periods that maximizes the total value of the blocks. Combinatorial search acceleration is achieved by representing a number of technological constraints in the form of global constraints.

scholarly journals Quantum-accelerated constraint programming

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 550
Author(s):  
Kyle E. C. Booth ◽  
Bryan O'Gorman ◽  
Jeffrey Marshall ◽  
Stuart Hadfield ◽  
Eleanor Rieffel
Keyword(s):  
Constraint Programming ◽  
Optimization Problems ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Global Constraints ◽  
Quantum Computers ◽  
Promising Candidate ◽  
Backtracking Search ◽  
Combinatorial Optimization Problems ◽  
Classical Quantum

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the alldifferent global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.

scholarly journals An Optimal Implementation on FPGA of a Hopfield Neural Network

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
W. Mansour ◽  
R. Ayoubi ◽  
H. Ziade ◽  
R. Velazco ◽  
W. EL Falou
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
High Performance ◽  
Optimization Problems ◽  
Parallel Architecture ◽  
Hopfield Neural Network ◽  
Noise Removal ◽  
Combinatorial Optimization Problems ◽  
Artificial Neural Network Ann ◽  
Optimal Implementation

The associative Hopfield memory is a form of recurrent Artificial Neural Network (ANN) that can be used in applications such as pattern recognition, noise removal, information retrieval, and combinatorial optimization problems. This paper presents the implementation of the Hopfield Neural Network (HNN) parallel architecture on a SRAM-based FPGA. The main advantage of the proposed implementation is its high performance and cost effectiveness: it requires O(1) multiplications and O(log⁡ N) additions, whereas most others require O(N) multiplications and O(N) additions.

scholarly journals On the Representation of Boolean and Real Functions as Hamiltonians for Quantum Computing

2021 ◽  
Vol 2 (4) ◽  
pp. 1-21
Author(s):  
Stuart Hadfield
Keyword(s):  
Quantum Computing ◽  
Boolean Functions ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Building Blocks ◽  
Constraint Satisfaction Problems ◽  
Boolean Formula ◽  
Combinatorial Optimization Problems ◽  
Compute Function ◽  
Real Functions

Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate optimization algorithm to combinatorial optimization problems. We show how such functions are naturally represented by Hamiltonians given as sums of Pauli Z operators (Ising spin operators) with the terms of the sum corresponding to the function’s Fourier expansion. For many classes of Boolean functions which are given by a compact description, such as a Boolean formula in conjunctive normal form that gives an instance of the satisfiability problem, it is #P-hard to compute its Hamiltonian representation, i.e., as hard as computing its number of satisfying assignments. On the other hand, no such difficulty exists generally for constructing Hamiltonians representing a real function such as a sum of local Boolean clauses each acting on a fixed number of bits as is common in constraint satisfaction problems. We show composition rules for explicitly constructing Hamiltonians representing a wide variety of Boolean and real functions by combining Hamiltonians representing simpler clauses as building blocks, which are particularly suitable for direct implementation as classical software. We further apply our results to the construction of controlled-unitary operators, and to the special case of operators that compute function values in an ancilla qubit register. Finally, we outline several additional applications and extensions of our results to quantum algorithms for optimization. A goal of this work is to provide a design toolkit for quantum optimization which may be utilized by experts and practitioners alike in the construction and analysis of new quantum algorithms, and at the same time to provide a unified framework for the various constructions appearing in the literature.

scholarly journals High-performance combinatorial optimization based on classical mechanics

2021 ◽  
Vol 7 (6) ◽  
pp. eabe7953
Author(s):  
Hayato Goto ◽  
Kotaro Endo ◽  
Masaru Suzuki ◽  
Yoshisato Sakai ◽  
Taro Kanao ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
High Speed ◽  
High Performance ◽  
Optimization Problems ◽  
Classical Mechanics ◽  
Massively Parallel ◽  
Optimal Solutions ◽  
Combinatorial Optimization Problems ◽  
Superconducting Circuit ◽  
Solution Accuracy

Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.

Sign in / Sign up

Export Citation Format

Share Document