Solving Clique Partitioning Problems: A Comparison of Models and Commercial Solvers

2021 ◽  
pp. 1-23
Author(s):  
Yu Du ◽  
Gary Kochenberger ◽  
Fred Glover ◽  
Haibo Wang ◽  
Mark Lewis ◽  
...  
Keyword(s):  
Linear Model ◽  
Quadratic Model ◽  
Problem Instance ◽  
Test Problems ◽  
Optimal Solutions ◽  
Problem Size ◽  
Clique Partitioning ◽  
Huge Impact ◽  
Partitioning Problems ◽  
The Right

Finding good solutions to clique partitioning problems remains a computational challenge. With rare exceptions, finding optimal solutions for all but small instances is not practically possible. However, choosing the most appropriate modeling structure can have a huge impact on what is practical to obtain from exact solvers within a reasonable amount of run time. Commercial solvers have improved tremendously in recent years and the combination of the right solver and the right model can significantly increase our ability to compute acceptable solutions to modest-sized problems with solvers like CPLEX, GUROBI and XPRESS. In this paper, we explore and compare the use of three commercial solvers on modest sized test problems for clique partitioning. For each problem instance, a conventional linear model from the literature and a relatively new quadratic model are compared. Extensive computational experience indicates that the quadratic model outperforms the classic linear model as problem size grows.

The Robustness of Two Common Heuristics for the p-Median Problem

1979 ◽  
Vol 11 (4) ◽  
pp. 373-380 ◽  
Author(s):  
K E Rosing ◽  
E L Hillsman ◽  
Hester Rosing-Vogelaar
Keyword(s):  
Heuristic Algorithms ◽  
Test Problems ◽  
Optimal Solutions ◽  
Problem Size ◽  
Median Problem ◽  
Robust Tests

Optimal p-median solutions were computed for six test problems on a network of forty-nine demand nodes and compared with solutions from two heuristic algorithms. Comparison of the optimal solutions with those from the Teitz and Bart heuristic indicates that this heuristic is very robust. Tests of the Maranzana heuristic, however, indicate that it is efficient only for small values of p (numbers of facilities) and that its robustness decreases rapidly as problem size increases.

scholarly journals Performance Comparison of OpenMP, MPI, and MapReduce in Practical Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Sol Ji Kang ◽  
Sang Yeon Lee ◽  
Keon Myung Lee
Keyword(s):  
Parallel Programming ◽  
Large Scale ◽  
Memory Systems ◽  
Performance Comparison ◽  
Benchmark Problems ◽  
Distributed Programming ◽  
Problem Size ◽  
Good Picture ◽  
Data Intensive ◽  
The Right

With problem size and complexity increasing, several parallel and distributed programming models and frameworks have been developed to efficiently handle such problems. This paper briefly reviews the parallel computing models and describes three widely recognized parallel programming frameworks: OpenMP, MPI, and MapReduce. OpenMP is the de facto standard for parallel programming on shared memory systems. MPI is the de facto industry standard for distributed memory systems. MapReduce framework has become the de facto standard for large scale data-intensive applications. Qualitative pros and cons of each framework are known, but quantitative performance indexes help get a good picture of which framework to use for the applications. As benchmark problems to compare those frameworks, two problems are chosen: all-pairs-shortest-path problem and data join problem. This paper presents the parallel programs for the problems implemented on the three frameworks, respectively. It shows the experiment results on a cluster of computers. It also discusses which is the right tool for the jobs by analyzing the characteristics and performance of the paradigms.

scholarly journals Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

2020 ◽  
Vol 61 (5) ◽  
pp. 1977-1999
Author(s):  
H. Fairclough ◽  
M. Gilbert
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Geometry Optimization ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Optimal Solutions ◽  
Problem Size ◽  
Solution Quality ◽  
Starting Point

AbstractTraditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from ‘crossover joints’ increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

Modelling the solar, geomagnetic and periodic variations of the ionosphere over Ethiopia

2020 ◽  
Vol 10 (1) ◽  
pp. 28-39
Author(s):  
T. Gogie
Keyword(s):  
Linear Model ◽  
Satellite Communication ◽  
Linear Time ◽  
Quadratic Model ◽  
Bahir Dar ◽  
Model Based ◽  
Time Series Modelling ◽  
Short Period ◽  
Period Variations ◽  
Periodic Components

A careful and continuous ionospheric modelling can significantly influence the performance of activities such as Positioning, Navigation and Timing services related with the Global Navigation Satellite System applications as well as the Earth Observations System, satellite communication and Space weather forecasting applications. In this paper, the linear time-series modelling that consists of the solar, geomagnetic and periodic components has been carried out on the daily ionospheric vTEC at two different Ethiopian GPS locations, at Arbaminch, ARMI (geographic 6.06ºN, 37.56ºE) and Bahir Dar, BDMT (geographic 11.60ºN, 37.38ºE), for the year 2012, 2014 and 2016 in the 24th solar cycle. The variations of vTEC due to the solar activities, geomagnetic activities and periodic oscillations have been explicitly investigated. The results confirmed that the correlation coefficient of the linear model based estimated vTEC and the observed GPS-vTEC is around 80% in the year 2014. Besides, solar activity is identified as the key component for the 27 days period variations of vTEC whereas geomagnetic activity is identified as the key component that influences the short-period variations of the daily average vTEC. In addition to the correlation analysis, the accuracy of the model has been assessed by comparing the International Reference Ionosphere (IRI 2016) model based vTEC and GPS-vTEC measurements as well as with the quadratic model based vTEC. Consequently, the linear model formulated with the solar, geomagnetic and periodic components significantly captured the variations (78-80%) of the observed vTEC compared with both the IRI 2016 and the quadratic models during the years 2012, 2014 and 2016. The comparison of the observed and predicted vTEC variations has also been examined using the continuous wavelet transform. The decomposed waves from the wavelet analysis have revealed that the predicted and observed vTEC have had simultaneous periods of variations specifically with the period of 27 days whereas the IRI 2016 could capture the short-period variations of vTEC. Moreover, the analysis from the transformed data in the year 2014 over both Arbaminch and Bahir Dar has indicated that the linear model based vTEC and the observed GPS-vTEC have had common pattern of variations with the period of 27 days that had lasted for 150 days (from day of the year 100 to 250).

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

scholarly journals Estimation of buckwheat leaf area by leaf dimensions

2021 ◽  
Vol 42 (3Supl1) ◽  
pp. 1529-1548
Author(s):  
Alberto Cargnelutti Filho ◽  
◽  
Rafael Vieira Pezzini ◽  
Ismael Mario Márcio Neu ◽  
Gabriel Elias Dumke ◽  
...  
Keyword(s):  
Leaf Area ◽  
Linear Model ◽  
Leaf Blade ◽  
Sowing Date ◽  
Quadratic Model ◽  
Digital Photo ◽  
Sowing Dates ◽  
Leaf Dimensions ◽  
Fagopyrum Esculentum Moench ◽  
Uniformity Trials

The objective of this work was to model and identify the best models for estimating the leaf area, determined by digital photos, of buckwheat (Fagopyrum esculentum Moench) of the cultivars IPR91-Baili and IPR92-Altar, as a function of length (L), width (W) or length x width product (LW) of the leaf blade. Ten uniformity trials (blank experiments) were carried out, five with IPR91-Baili cultivar and five with IPR92-Altar cultivar. The trials were performed on five sowing dates. In each trial and cultivar, expanded leaves were collected at random from the lower, middle and upper segments of the plants, totaling 1,815 leaves. In these 1,815 leaves, L and W were measured and the LW of the leaf blade was calculated, which were used as independent variables in the model. The leaf area of each leaf was determined using the digital photo method (Y), which was used as a dependent variable of the model. For each sowing date, cultivar and thirds of the plant, 80% of the leaves (1,452 leaves) were randomly separated for the generation of the models and 20% of the leaves (363 leaves) for the validation of the models of leaf area estimation as a function of linear dimensions. For buckwheat, IPR91-Baili and IPR92-Altar cultivars, the quadratic model (Ŷ = 0.5217 + 0.6581LW + 0.0004LW2, R2 = 0.9590), power model (Ŷ = 0.6809LW1.0037, R2 = 0.9587), linear model (Ŷ = 0.0653 + 0.6892LW, R2 = 0.9587) and linear model without intercept (Ŷ = 0.6907LW, R2 = 0.9587) are indicated for the estimation of leaf area determined by digital photos (Y) based on the LW of the leaf blade (x), and, preferably, the linear model without intercept can be used, due to its greater simplicity.

scholarly journals Alternative Method for Estimating the Maintenance Cost of Roads in Anambra State, Nigeria

2020 ◽  
pp. 31-38
Author(s):  
Godspower Onyekachukwu Ekwueme ◽  
John Obatarhe Emunefe ◽  
Nkechi Udochukwu Otty ◽  
Charles Okechukwu Aronu
Keyword(s):  
Linear Model ◽  
Secondary Data ◽  
Quadratic Model ◽  
Maintenance Cost ◽  
Future Studies ◽  
Anambra State ◽  
Construction Company ◽  
Alternative Method ◽  
Proposed Model ◽  
Better Than

Aims: This study proposed an alternative method for the estimation of maintenance cost of roads in Anambra State, Nigeria. The proposed method referred to as the permuted quadratic model (PQM) involves permuting of the dependent variable of the quadratic model. Place and Duration of Study: The data used in this study was secondary data sourced from the records department of consolidated construction company asphalt plant Anambra state, Nigeria from 2004 to 2019. Methodology: The linear regression model and the permuted quadratic model were used to analyze the data for the study. Results: The result found that 74.0% correlation exists between the observed maintenance cost of roads and the predicted maintenance cost of roads using the linear model while the predicted maintenance cost of roads using the permuted quadratic model has 75.8% correlation with the observed maintenance cost of roads. This result indicates that the proposed permuted quadratic model performed better than the linear model for the estimation of the maintenance cost of roads in Anambra State. Conclusion: The study recommends the proposed model for the estimation of maintenance cost of roads in Anambra State until future studies prove otherwise.

scholarly journals NUTRITION IN AYURVEDA WITH SPECIAL REFERENCE TO NITYASEVANEEYA AND ANITYASEVANEEYA DRAVYAS

2021 ◽  
pp. 74-78
Author(s):  
Parvathy B ◽  
Neelakanta J Sajjanar ◽  
Gopalakrishna G
Keyword(s):  
Food Habits ◽  
Food Choices ◽  
Detailed Review ◽  
Food Items ◽  
Regular Consumption ◽  
Contemporary Science ◽  
Huge Impact ◽  
Major Factors ◽  
The Right ◽  
Lifestyle Diseases

It is an undeniable fact that food choices make a huge impact on health of an individual. 21st century has witnessed an increase in incidences of non-communicable chronic diseases also known as lifestyle diseases. One of the major factors responsible for it is the unhealthy food habits. Thus, it is the need of the hour to understand more about the right food choices for daily nutrition. Ayurveda explains about of nutrition under Pathyapathya. Ayurveda emphasizes the importance of Pathyapathya in the maintenance of health as well as management of diseases. Nityasevaneeya dravyas, are the food items which are ideal for regular use like green gram (Mudga), ghee (Go ghruta), honey (Madhu). These help to promote and maintain health as well as prevent diseases. At the same time Anitya sevaneeya dravyas, are those food articles which are not suitable for regular use like Paneer (Kurchika), curd (Dadhi), black gram (Masha). These food items on regular consumption can lead to many diseases. In this study a detailed review of each drug mentioned under Nitya sevaneeya and Anityasevaneeya dravyas both in Ayurveda and contemporary science are done. Review indents to highlight the scientific background behind each food article to re-establish their relevance in today’s time.

scholarly journals The relationship between problem size and fixation patterns during addition, subtraction, multiplication, and division

2016 ◽  
Vol 2 (2) ◽  
pp. 91-115 ◽  
Author(s):  
Evan T. Curtis ◽  
Matthew G. Huebner ◽  
Jo-Anne LeFevre
Keyword(s):  
Eye Movements ◽  
Eye Tracking ◽  
Cognitive Processing ◽  
Mental Arithmetic ◽  
Problem Size ◽  
Single Digit ◽  
Simple Arithmetic ◽  
Division Problems ◽  
The Right ◽  
The Relationship

Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8) and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6). Participants (N = 109) solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

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