scholarly journals Graph coloring using the reduced quantum genetic algorithm

2022 ◽  
Vol 7 ◽  
pp. e836
Author(s):  
Sebastian Mihai Ardelean ◽  
Mihai Udrescu
Keyword(s):  
Genetic Algorithm ◽  
Graph Coloring ◽  
Optimization Problems ◽  
Edge Coloring ◽  
Np Hard ◽  
Quantum Genetic Algorithm ◽  
Graph Coloring Problem ◽  
Minimum Number ◽  
Hard Problems ◽  
Noise Models

Genetic algorithms (GA) are computational methods for solving optimization problems inspired by natural selection. Because we can simulate the quantum circuits that implement GA in different highly configurable noise models and even run GA on actual quantum computers, we can analyze this class of heuristic methods in the quantum context for NP-hard problems. This paper proposes an instantiation of the Reduced Quantum Genetic Algorithm (RQGA) that solves the NP-hard graph coloring problem in O(N1/2). The proposed implementation solves both vertex and edge coloring and can also determine the chromatic number (i.e., the minimum number of colors required to color the graph). We examine the results, analyze the algorithm convergence, and measure the algorithm's performance using the Qiskit simulation environment. Our Reduced Quantum Genetic Algorithm (RQGA) circuit implementation and the graph coloring results show that quantum heuristics can tackle complex computational problems more efficiently than their conventional counterparts.

scholarly journals Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
J. Cervantes-Ojeda ◽  
M. Gómez-Fuentes ◽  
D. González-Moreno ◽  
M. Olsen
Keyword(s):  
Genetic Algorithm ◽  
Upper Bound ◽  
Connected Graph ◽  
Edge Coloring ◽  
Np Hard ◽  
The Family ◽  
Minimum Number ◽  
The One ◽  
Vertex Disjoint ◽  
Rainbow Coloring

Arainbowt-coloringof at-connected graphGis an edge coloring such that for any two distinct verticesuandvofGthere are at leasttinternally vertex-disjoint rainbow(u,v)-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbowt-colorings of the family of Moore cages with girth six(t;6)-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a(4;6)-cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbowt-colorings with a small number of colors.

scholarly journals Nanolaser-based emulators of spin Hamiltonians

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4193-4198 ◽  
Author(s):  
Midya Parto ◽  
William E. Hayenga ◽  
Alireza Marandi ◽  
Demetrios N. Christodoulides ◽  
Mercedeh Khajavikhan
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Exchange Interactions ◽  
Np Hard ◽  
Spin Models ◽  
Geometric Frustration ◽  
Spin Hamiltonians ◽  
Hard Problems ◽  
On Chip ◽  
Classical Spin Models

AbstractFinding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.

scholarly journals Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

2020 ◽  
Vol 10 (6) ◽  
pp. 2075 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Inequality Constraints ◽  
Optimization Methods ◽  
Ordinal Optimization ◽  
Np Hard ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Hard Problems ◽  
Np Hard Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

scholarly journals Optimization of Network Coding Resources Based on Improved Quantum Genetic Algorithm

Photonics ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 502
Author(s):  
Tianyang Liu ◽  
Qiang Sun ◽  
Huachun Zhou ◽  
Qi Wei
Keyword(s):  
Genetic Algorithm ◽  
Network Coding ◽  
Topological Structure ◽  
Rotation Angle ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Resource Optimization ◽  
Quantum Genetic Algorithm ◽  
Adjustment Mechanism ◽  
Adaptive Adjustment

The problem of network coding resource optimization with a known topological structure is NP-hard. Traditional quantum genetic algorithms have the disadvantages of slow convergence and difficulty in finding the optimal solution when dealing with this problem. To overcome these disadvantages, this paper proposes an adaptive quantum genetic algorithm based on the cooperative mutation of gene number and fitness (GNF-QGA). This GNF-QGA adopts the rotation angle adaptive adjustment mechanism. To avoid excessive illegal individuals, an illegal solution adjustment mechanism is added to the GNF-QGA. A solid demonstration was provided that the proposed algorithm has a fast convergence speed and good optimization capability when solving network coding resource optimization problems.

scholarly journals Application of genetic algorithm to industrial scheduling and problems of parameters evaluation

2021 ◽  
Vol 47 ◽  
Author(s):  
Edgaras Šakurovas ◽  
Narimantas Listopadskis
Keyword(s):  
Genetic Algorithm ◽  
Job Shop ◽  
Flow Shop ◽  
Np Hard ◽  
Scheduling Problems ◽  
Optimal Parameters ◽  
Algorithm Performance ◽  
Hard Problems ◽  
Np Hard Problems ◽  
Real World Problems

Genetic algorithms are widely used in various mathematical and real world problems. They are approximate metaheuristic algorithms, commonly used for solving NP-hard problems in combinatorial optimisation. Industrial scheduling is one of the classical NP-hard problems. We analyze three classical industrial scheduling problems: job-shop, flow-shop and open-shop. Canonical genetic algorithm is applied for those problems varying its parameters. We analyze some aspects of parameters such as selecting optimal parameters of algorithm, influence on algorithm performance. Finally, three strategies of algorithm – combination of parameters and new conceptualmodel of genetic algorithm are proposed.

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