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.

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.

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 On Chamfer Distances on the Square and Body-Centered Cubic Grids: An Operational Research Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Gergely Kovács ◽  
Benedek Nagy ◽  
Gergely Stomfai ◽  
Neşet Deni̇z Turgay ◽  
Béla Vizvári
Keyword(s):  
Linear Programming ◽  
Operational Research ◽  
Optimization Problems ◽  
Shortest Paths ◽  
Optimal Solution ◽  
The Body ◽  
Research Approach ◽  
Body Centered Cubic ◽  
Solid State Physics ◽  
Chamfer Distances

Linear programming is used to solve optimization problems. Thus, finding a shortest path in a grid is a good target to apply linear programming. In this paper, specific bipartite grids, the square and the body-centered cubic grids are studied. The former is represented as a “diagonal square grid” having points with pairs of either even or pairs of odd coordinates (highlighting the bipartite feature). Therefore, a straightforward generalization of the representation describes the body-centered cubic grid in 3D. We use chamfer paths and chamfer distances in these grids; therefore, weights for the steps between the closest neighbors and steps between the closest same type points are fixed, and depending on the weights, various paths could be the shortest one. The vectors of the various neighbors form a basis if they are independent, and their number is the same as the dimension of the space studied. Depending on the relation of the weights, various bases could give the optimal solution and various steps are used in the shortest paths. This operational research approach determines the optimal paths as basic feasible solutions of a linear programming problem. A directed graph is given containing the feasible bases as nodes and arcs with conditions on the used weights such that the simplex method may step from one feasible basis to another one. Thus, the optimal bases can be determined, and they are summarized in two theorems. If the optimal solution is not integer, then the Gomory cut is applied and the integer optimal solution is reached after only one Gomory iteration. Chamfer distances are frequently used in image processing and analysis as well as graphics-related subjects. The body-centered cubic grid, which is well-known in solid state physics, material science, and crystallography, has various applications in imaging and graphics since less samples are needed to represent the signal in the same quality than on the cubic grid. Moreover, the body-centered cubic grid has also a topological advantage over the cubic grid, namely, the neighbor Voronoi cells always share a full face.

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.

On Solution of a Certain Integer Programming Problem of a Specific Form

1998 ◽  
Vol 30 (4-5) ◽  
pp. 115-120
Author(s):  
Ivan V. Sergienko ◽  
V. A. Roshchin
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Specific Form ◽  
Integer Programming Problem

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.

TWO BI-OBJECTIVE OPTIMIZATION MODELS FOR COMPETITIVE LOCATION PROBLEMS

2006 ◽  
Vol 05 (03) ◽  
pp. 531-543 ◽  
Author(s):  
FENGMEI YANG ◽  
GUOWEI HUA ◽  
HIROSHI INOUE ◽  
JIANMING SHI
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Integer Program ◽  
Location Problems ◽  
Optimization Models ◽  
Competitive Location ◽  
Integer Programming Problem ◽  
Single Objective ◽  
Parametric Integer Programming

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

scholarly journals Multitarget Tracking Algorithm Based on Adaptive Network Graph Segmentation in the Presence of Measurement Origin Uncertainty

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3791
Author(s):  
Tianli Ma ◽  
Song Gao ◽  
Chaobo Chen ◽  
Xiaoru Song
Keyword(s):  
Shortest Path ◽  
Clustering Algorithm ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Tracking Algorithm ◽  
Multitarget Tracking ◽  
Integer Programming Problem ◽  
Tracking Accuracy ◽  
Network Graph ◽  
Adaptive Network

To deal with the problem of multitarget tracking with measurement origin uncertainty, the paper presents a multitarget tracking algorithm based on Adaptive Network Graph Segmentation (ANGS). The multitarget tracking is firstly formulated as an Integer Programming problem for finding the maximum a posterior probability in a cost flow network. Then, a network structure is partitioned using an Adaptive Spectral Clustering algorithm based on the Nyström Method. In order to obtain the global optimal solution, the parallel A* search algorithm is used to process each sub-network. Moreover, the trajectory set is extracted by the Track Mosaic technique and Rauch–Tung–Striebel (RTS) smoother. Finally, the simulation results achieved for different clutter intensity indicate that the proposed algorithm has better tracking accuracy and robustness compared with the A* search algorithm, the successive shortest-path (SSP) algorithm and the shortest path faster (SPFA) algorithm.

Enhanced UAS Surveillance Using a Video Utility Metric

2013 ◽  
Vol 01 (02) ◽  
pp. 277-296 ◽  
Author(s):  
Peter C. Niedfeldt ◽  
Brandon T. Carroll ◽  
Joel A. Howard ◽  
Randal W. Beard ◽  
Bryan S. Morse ◽  
...  
Keyword(s):  
Planning Process ◽  
Optimal Path ◽  
Optimal Solution ◽  
Flight Test ◽  
Video Stream ◽  
Flight Path ◽  
Optimal Path Planning ◽  
Planning Approach ◽  
Human Operators ◽  
Imaging Sensors

A successful mission for an Unmanned Air System (UAS) often depends on the ability of human operators to utilize data collected from onboard imaging sensors. Many hours are spent preparing and executing flight objectives, putting a tremendous burden on human operators both before and during the flight. We seek to automate the planning process to reduce the workload for UAS operators while also optimizing the quality of the collected video stream. We first propose a metric based on an existing image utility metric to estimate the utility of video captured by onboard cameras. We then use this metric to not only plan the UAS flight path, but also the path of the camera's optical axis projected along the terrain and the zoom level. Since computing an optimal solution is NP-hard and therefore infeasible, we subsequently describe a staged sub-optimal path planning approach to autonomously plan the UAS flight path and sensor schedule. We apply these algorithms to precompute UAS and sensor paths for a surveillance mission over a specified region. Simulated and actual flight test results are included.

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