Solving Mixed-Binary Optimization Problems for Groundwater Management

2003 ◽  
Author(s):  
David P. Ahlfeld
Keyword(s):  
Groundwater Management ◽  
Optimization Problems ◽  
Binary Optimization

Decision Diagram Decomposition for Quadratically Constrained Binary Optimization

2020 ◽  
Author(s):  
David Bergman ◽  
Leonardo Lozano
Keyword(s):  
Benders Decomposition ◽  
Optimization Problems ◽  
State Of The Art ◽  
Cutting Plane Algorithm ◽  
Decision Diagrams ◽  
Quadratic Constraints ◽  
Binary Optimization ◽  
Limited Size ◽  
Quadratic Matrix ◽  
Quadratically Constrained

In recent years the use of decision diagrams within the context of discrete optimization has proliferated. This paper continues this expansion by proposing the use of decision diagrams for modeling and solving binary optimization problems with quadratic constraints. The model proposes the use of multiple decision diagrams to decompose a quadratic matrix so that each individual diagram has provably limited size. The decision diagrams are then linked through channeling constraints to ensure that the solution represented is consistent across the decision diagrams and that the original quadratic constraints are satisfied. The resulting family of decision diagrams are optimized over by a dedicated cutting-plane algorithm akin to Benders decomposition. The approach is general, in that commercial integer programming solvers can readily apply the technique. A thorough experimental evaluation on both benchmark and synthetic instances exhibits that the proposed decision diagram reformulation provides significant improvements over current methods for quadratic constraints in state-of-the-art solvers.

scholarly journals Black box scatter search for general classes of binary optimization problems

2010 ◽  
Vol 37 (11) ◽  
pp. 1977-1986 ◽  
Author(s):  
Francisco Gortázar ◽  
Abraham Duarte ◽  
Manuel Laguna ◽  
Rafael Martí
Keyword(s):  
Optimization Problems ◽  
Scatter Search ◽  
Black Box ◽  
Binary Optimization

scholarly journals Quadratic reformulations of nonlinear binary optimization problems

2016 ◽  
Vol 162 (1-2) ◽  
pp. 115-144 ◽  
Author(s):  
Martin Anthony ◽  
Endre Boros ◽  
Yves Crama ◽  
Aritanan Gruber
Keyword(s):  
Optimization Problems ◽  
Binary Optimization

scholarly journals Grover Adaptive Search for Constrained Polynomial Binary Optimization

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 428
Author(s):  
Austin Gilliam ◽  
Stefan Woerner ◽  
Constantin Gonciulea
Keyword(s):  
Optimization Problems ◽  
Adaptive Search ◽  
Binary Optimization ◽  
Combinatorial Optimization Problems ◽  
Quadratic Unconstrained Binary Optimization ◽  
Speed Up ◽  
Near Term ◽  
Quantum Arithmetic ◽  
Portfolio Optimization Problem ◽  
Special Case

In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a quadratic speed-up for combinatorial optimization problems compared to brute force search. However, this requires the development of efficient oracles to represent problems and flag states that satisfy certain search criteria. In general, this can be achieved using quantum arithmetic, however, this is expensive in terms of Toffoli gates as well as required ancilla qubits, which can be prohibitive in the near-term. Within this work, we develop a way to construct efficient oracles to solve CPBO problems using GAS algorithms. We demonstrate this approach and the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation and experimental results obtained on real quantum hardware. However, our approach applies to higher-degree polynomial objective functions as well as constrained optimization problems.

scholarly journals Tree-Seed Algorithm for Large-Scale Binary Optimization

2018 ◽  
Vol 3 (1) ◽  
pp. 48 ◽  
Author(s):  
Ahmet Cevahir Cinar ◽  
Hazim Iscan ◽  
Mustafa Servet Kiran
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Logic Gate ◽  
Continuous Optimization ◽  
Population Based ◽  
Benchmark Problems ◽  
Binary Optimization ◽  
Continuous Optimization Problems ◽  
Computation Algorithms ◽  
Tree Seed

Population-based swarm or evolutionary computation algorithms in optimization are attracted the interest of the researchers due their simple structure, optimization performance, easy-adaptation. Binary optimization problems can be also solved by using these algorithms. This paper focuses on solving large scale binary optimization problems by using Tree-Seed Algorithm (TSA) proposed for solving continuous optimization problems by imitating relationship between the trees and their seeds in nature. The basic TSA is modified by using xor logic gate for solving binary optimization problems in this study. In order to investigate the performance of the proposed algorithm, the numeric benchmark problems with the different dimensions are considered and obtained results show that the proposed algorithm produces effective and comparable solutions in terms of solution quality.Keywords: binary optimization, tree-seed algorithm, xor-gate, large-scale optimization

scholarly journals XOR Binary Gravitational Search Algorithm with Repository: Industry 4.0 Applications

2020 ◽  
Vol 10 (18) ◽  
pp. 6451
Author(s):  
Mojtaba Ahmadieh Khanesar ◽  
Ridhi Bansal ◽  
Giovanna Martínez-Arellano ◽  
David T. Branson
Keyword(s):  
Industry 4.0 ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Superior Performance ◽  
Binary Particle Swarm Optimization ◽  
Binary Optimization ◽  
Diverse Range ◽  
Digital Twin ◽  
Gravitational Search

Industry 4.0 is the fourth generation of industry which will theoretically revolutionize manufacturing methods through the integration of machine learning and artificial intelligence approaches on the factory floor to obtain robustness and speed-up process changes. In particular, the use of the digital twin in a manufacturing environment makes it possible to test such approaches in a timely manner using a realistic 3D environment that limits incurring safety issues and danger of damage to resources. To obtain superior performance in an Industry 4.0 setup, a modified version of a binary gravitational search algorithm is introduced which benefits from an exclusive or (XOR) operator and a repository to improve the exploration property of the algorithm. Mathematical analysis of the proposed optimization approach is performed which resulted in two theorems which show that the proposed modification to the velocity vector can direct particles to the best particles. The use of repository in this algorithm provides a guideline to direct the particles to the best solutions more rapidly. The proposed algorithm is evaluated on some benchmark optimization problems covering a diverse range of functions including unimodal and multimodal as well as those which suffer from multiple local minima. The proposed algorithm is compared against several existing binary optimization algorithms including existing versions of a binary gravitational search algorithm, improved binary optimization, binary particle swarm optimization, binary grey wolf optimization and binary dragonfly optimization. To show that the proposed approach is an effective method to deal with real world binary optimization problems raised in an Industry 4.0 environment, it is then applied to optimize the assembly task of an industrial robot assembling an industrial calculator. The optimal movements obtained are then implemented on a real robot. Furthermore, the digital twin of a universal robot is developed, and its path planning is done in the presence of obstacles using the proposed optimization algorithm. The obtained path is then inspected by human expert and validated. It is shown that the proposed approach can effectively solve such optimization problems which arises in Industry 4.0 environment.

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