scholarly journals Applying the Hubbard-Stratonovich Transformation to Solve Scheduling Problems Under Inequality Constraints With Quantum Annealing

2021 ◽  
Vol 9 ◽  
Author(s):  
Sizhuo Yu ◽  
Tahar Nabil
Keyword(s):  
Integer Programming ◽  
Penalty Method ◽  
Real Life ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Tunneling Effect ◽  
Use Case ◽  
Integer Programming Problem ◽  
Scheduling Problems ◽  
Quantum Annealing

Quantum annealing is a global optimization algorithm that uses the quantum tunneling effect to speed-up the search for an optimal solution. Its current hardware implementation relies on D-Wave’s Quantum Processing Units, which are limited in terms of number of qubits and architecture while being restricted to solving quadratic unconstrained binary optimization (QUBO) problems. Consequently, previous applications of quantum annealing to real-life use cases have focused on problems that are either native QUBO or close to native QUBO. By contrast, in this paper we propose to tackle inequality constraints and non-quadratic terms. We demonstrate how to handle them with a realistic use case-a bus charging scheduling problem. First, we reformulate the original integer programming problem into a QUBO with the penalty method and directly solve it on a D-Wave machine. In a second approach, we dualize the problem by performing the Hubbard-Stratonovich transformation. The dual problem is solved indirectly by combining quantum annealing and adaptive classical gradient-descent optimizer. Whereas the penalty method is severely limited by the connectivity of the realistic device, we show experimentally that the indirect approach is able to solve problems of a larger size, offering thus a better scaling. Hence, the implementation of the Hubbard-Stratonovich transformation carried out in this paper on a scheduling use case suggests that this approach could be investigated further and applied to a variety of real-life integer programming problems under multiple constraints to lower the cost of mapping to QUBO, a key step towards the near-term practical application of quantum computing.

scholarly journals The Magnetic Bead Computing Model of the 0-1 Integer Programming Problem Based on DNA Cycle Hybridization

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Rujie Xu ◽  
Zhixiang Yin ◽  
Zhen Tang ◽  
Jing Yang ◽  
Jianzhong Cui ◽  
...  
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Magnetic Beads ◽  
Specific Binding ◽  
Optimal Solution ◽  
High Sensitivity ◽  
Magnetic Bead ◽  
Integer Programming Problem ◽  
Computing Model ◽  
Dna Strands

Magnetic beads and magnetic Raman technology substrates have good magnetic response ability and surface-enhanced Raman technology (SERS) activity. Therefore, magnetic beads exhibit high sensitivity in SERS detection. In this paper, DNA cycle hybridization and magnetic bead models are combined to solve 0-1 integer programming problems. First, the model maps the variables to DNA strands with hairpin structures and weights them by the number of hairpin DNA strands. This result can be displayed by the specific binding of streptavidin and biotin. Second, the constraint condition of the 0-1 integer programming problem can be accomplished by detecting the signal intensity of the biological barcode to find the optimal solution. Finally, this model can be used to solve the general 0-1 integer programming problem and has more extensive applications than the previous DNA computing model.

Application of Mixed-Integer Programming and Dispatching Rules on Parallel Machine Scheduling with Inserted Idle Time

2013 ◽  
Vol 437 ◽  
pp. 748-751
Author(s):  
Chi Yang Tsai ◽  
Yi Chen Wang
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Parallel Machines ◽  
Optimal Solution ◽  
Parallel Machine Scheduling ◽  
Idle Time ◽  
Dispatching Rules ◽  
Mixed Integer ◽  
Scheduling Problems

This research considers the problem of scheduling jobs on unrelated parallel machines with inserted idle times to minimize the earliness and tardiness. The aims at investigating how particular objective value can be improved by allowing machine idle time and how quality solutions can be more effectively obtained. Two mixed-integer programming formulations combining with three dispatching rules are developed to solve such scheduling problems. They can easy provide the optimal solution to problem involving about nine jobs and four machines. From the results of experiments, it is found that: (1) the inserted idle times decreases objective values more effectively; (2) three dispatching rules are very competitive in terms of efficiency and quality of solutions.

scholarly journals Hybrid Jaya Algorithm for Solving Multi-Objective 0-1 Integer Programming Problem

2019 ◽  
Vol 9 (2) ◽  
pp. 4867-4871
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Membership Function ◽  
Optimal Solution ◽  
Integer Programming Problem ◽  
Jaya Algorithm ◽  
Data Set ◽  
Suggested Algorithm ◽  
Multi Objective ◽  
Improved Algorithm

The aim of this paper is to find the optimal solution of complex multi-objective 0-1 integer programming problem(IPP) where as other evolutionary approaches are fails to achieve optimal solution or it may take huge efforts for computation. This paper presents the Hybrid Jaya algorithm for solving Multi-objective 0-1 IPP with the use of exponential membership function. In this work, we have improved the Jaya algorithm by bring in the conception of binary and exponential membership function. To established the effectualness of the suggested algorithm, one mathematical illustration is given with a data set from the practical and sensible state. At the end, the response of the improved algorithm is compared with other reported algorithms and we found that the suggested algorithm is evenly good or better for obtaining the solution of multi-objective 0-1 IPP.

scholarly journals OPTIMASI PENJADWALAN WAKTU KERJA MENGGUNAKAN INTEGER PROGRAMMING

2019 ◽  
Vol 7 (2) ◽  
pp. 51-55
Author(s):  
Windra Tahir ◽  
Djihad Wungguli ◽  
Muhamad Rezky Friesta Payu
Keyword(s):  
Integer Programming ◽  
Optimization Technique ◽  
Linear Constraint ◽  
Crumb Rubber ◽  
Integer Programming Problem ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Integer Variables ◽  
Determining Factors ◽  
Linear Objective Functions

Scheduling workers is one of the problems faced by every company. The regulations set by the company, the availability of the number of workers, and the division of labor are the determining factors in the scheduling system. This worker scheduling problem can be modeled as an Integer Programming problem. Integer Programming is an optimization technique with linear objective functions, linear constraint functions, and integer variables. This paper discusses the formulation of worker scheduling problems in the form of Integer Programming with workers in companies engaged in the production of Crumb Rubber with the objective function of minimizing the number of workers employed. The next model is implemented using the help of LINGO 11.0 software. The implementation results show that the model is able to produce optimal employee schedules.

scholarly journals Discrete Optimization: The Case of Generalized BCC Lattice

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 208
Author(s):  
Gergely Kovács ◽  
Benedek Nagy ◽  
Gergely Stomfai ◽  
Neşet Deniz Turgay ◽  
Béla Vizvári
Keyword(s):  
Integer Programming ◽  
Optimal Path ◽  
Optimal Solution ◽  
Linear Programming Relaxation ◽  
Integer Programming Problem ◽  
Body Centered Cubic ◽  
Solid State Physics ◽  
Negative Part ◽  
Integer Points ◽  
Bcc Lattice

Recently, operations research, especially linear integer-programming, is used in various grids to find optimal paths and, based on that, digital distance. The 4 and higher-dimensional body-centered-cubic grids is the nD (n≥4) equivalent of the 3D body-centered cubic grid, a well-known grid from solid state physics. These grids consist of integer points such that the parity of all coordinates are the same: either all coordinates are odd or even. A popular type digital distance, the chamfer distance, is used which is based on chamfer paths. There are two types of neighbors (closest same parity and closest different parity point-pairs), and the two weights for the steps between the neighbors are fixed. Finding the minimal path between two points is equivalent to an integer-programming problem. First, we solve its linear programming relaxation. The optimal path is found if this solution is integer-valued. Otherwise, the Gomory-cut is applied to obtain the integer-programming optimum. Using the special properties of the optimization problem, an optimal solution is determined for all cases of positive weights. The geometry of the paths are described by the Hilbert basis of the non-negative part of the kernel space of matrix of steps.

Regular Expression Learning from Positive Examples Based on Integer Programming

2020 ◽  
Vol 30 (10) ◽  
pp. 1443-1479
Author(s):  
Juntao Gao ◽  
Yingqian Zhang
Keyword(s):  
Integer Programming ◽  
Regular Expression ◽  
Real Life ◽  
Optimal Solution ◽  
Linear Program ◽  
Experimental Results ◽  
Integer Linear Program ◽  
Regular Expressions ◽  
Novel Method ◽  
Learning From Positive Examples

This paper presents a novel method to infer regular expressions from positive examples. The method consists of a candidate’s construction phase and an optimization phase. We first propose multiscaling sample augmentation to capture the cycle patterns from single examples during the candidate’s construction phase. We then use common substrings to build regular expressions that capture patterns across multiple examples, and we show this algorithm is more general than those based on common prefixes or suffixes. Furthermore, we propose a pruning mechanism to improve the efficiency of useful common substring mining, which is an important part of common substring-based expression building algorithm. Finally, in the optimization phase, we model the problem of choosing a set of regular expressions with the lowest cost as an integer linear program, which can be solved to obtain the optimal solution. The experimental results on synthetic and real-life samples demonstrate the effectiveness of our approach in inferring concise and semantically meaningful regular expressions for string datasets.

scholarly journals Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Daniel Vert ◽  
Renaud Sirdey ◽  
Stéphane Louise
Keyword(s):  
Simulated Annealing ◽  
Polynomial Time ◽  
Optimal Solution ◽  
Quantum Computers ◽  
Quantum Annealing ◽  
Maximum Cardinality ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Wave Device ◽  
D Wave

AbstractThis paper experimentally investigates the behavior of analog quantum computers as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem which is specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave “Washington” (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggest that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and hence provides additional evidences suggesting that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality. Additionally, we investigate the extent to which the qubits interconnection topologies explains these latter experimental results. In particular, we provide evidences that the sparsity of these topologies which, as such, lead to QUBO problems of artificially inflated sizes can partly explain the aforementioned disappointing observations. Therefore, this paper hints that denser interconnection topologies are necessary to unleash the potential of the quantum annealing approach.

scholarly journals A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Godfrey Chagwiza ◽  
Chipo Chivuraise ◽  
Christopher T. Gadzirayi
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Moringa Oleifera ◽  
Bat Algorithm ◽  
Mixed Integer ◽  
Poultry Feed ◽  
Integer Programming Problem ◽  
Optimum Solution ◽  
Mixed Integer Programming Problem ◽  
Number Of Iterations

In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.

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