Optimization Techniques Books
Darios Uclaray
Do you know of a good book on linear programming? To be more specific, i am taking linear optimization class and my textbook sucks. Teacher is not too involved in this class so can't get too much help from him either,Any help will be appreciated.Thank you
The other classics besides Winston are Hillier and Lieberman's Introduction to Operations Research and Chvtal's Linear Programmming. I learned linear programming out of Bob Vanderbei's Linear Programming: Foundations and Extensions, which is also a fine book. The last time I taught linear programming I used Dave Rader's new book, Deterministic Operations Research, and was happy with it.
As for a comparison, Winston focuses on how the different methods work and gives lots of examples but doesn't spend much time on theory. Hillier and Lieberman is at a slightly higher level than Winston, with a more leisurely pace and a little more theory but with fewer examples. Chvtal and Vanderbei have a more noticeable focus on the theory. Rader takes a different approach in that the simplex method does not appear until about halfway through the book. Instead, he spends a lot of time early on algorithm design and on what an algorithm for solving linear programs might look like so that when you finally do see the simplex method the reaction is closer to "Of course" than to "Where in the world did that come from?" He doesn't do the tableau form of the simplex method, which, while a plus in my opinion, may make it hard to understand his version of the simplex method if you're used to the tableau.
Many LP books spend little time on how to construct linear programming models (i.e, how to come up with variables, an objective function, and constraints that describe the problem you're trying to solve). Of these five, Winston and Rader discuss construction of LP models the most.
This is more a books of application ( with proofs ) full of algorithms using linear and integer programming, duality, also unimodularity, Chvatal-Gomory cuts and solving TSP with various methods. Both books are complementary ;) I recommend starting with first one and read few chapters of Combinatorial Optimization to get another look at things.
I'm taking a class that uses Linear Programming with Matlab, but it's really hard to read. I got Linear Programming: Methods and Applications to supplement it and it's much more readable. It's targeted at undergraduates, I guess. It has a lot of proofs, but most of the text is explanatory.
Linear Programming : An Introduction To Finite Improvement Algorithmsby Daniel Solow.It is also a good introduction to the theme. Appendix discusses about the other algorithms.His book develops proof aspect systematically.
I was reading Modern Optimization with R (Use R!) and wondering if a book like this exists in Python too? To be precise something that covers stochastic gradient descent and other advanced optimization techniques. Many thanks!
You should be able to translate code written in one language -- even pseudo-code -- to another, so I see no reason to avoid books for R. If you want one specifically for python, there's Machine Learning in Action by Peter Harrington.
Bentham is offering subject-based scholarly content collections which are tailored to meet specific research needs. Researchers can access related articles from current and back volumes by purchasing access to these collections. Subscribers will also have access to new articles as soon as they are published and added to these collections. With new articles being added to these collections on a daily basis, the collections serve as an ideal tool to keep researchers updated with new developments in the respective fields.
We deal with a parametric set-valued optimization problem (in brief, PSOP), whereset-valued functions (in brief, SVFs) are used for the constraint and objective functions. Weuse the idea of higher-order p-cone convexity of SVFs (introduced by Das and Nahak [1] as ageneralization of cone convex SVFs. We provide the Karush-Kuhn-Tucker (in brief, KKT)criteria of sufficiency for the presence of the minimizers of the PSOPs under higher-order p-cone convexity assumption. Further, we constitute the duality models of Mond-Weir kind anddemonstrate the strong, weak, and converse duality theorems under higher-order contingentepi-derivative and higher-order p-cone convexity assumption to a couple of set-valuedoptimization problems (in brief, SOPs). We provide some examples to justify our results. As aspecial case, our results reduce to the existing ones of scalar-valued parametric optimizationproblems
The primary objective of the study is to investigate the trigeneration system for thesimultaneous production of power, heating, and cooling, driven by solar power towersemploying molten salt as the heat transfer fluid. A comparative analysis is provided betweenrefrigerants (LiNO3-H2O and LiBr-H2O), so as to evaluate the best thermodynamicperformance for the vapor absorption refrigeration system among them. A novel concept ofuncertainty analysis is introduced which is a prime instance in this research area so as to providemuch better results with precision removing all human and machine errors stipulated to be 5.34% which is to be found in the desired range. Combined energy and exergy analyses areperformed to investigate the variation in efficienices while altering various performanceparameters for the trigeneration system. The highest exergy destruction was found to be 33.6%by the central receiver, 24.9% by heliostat, and 7.8% by heat recovery steam generators. Thehighest energy and exergy efficiencies (62.6% and 20.6%) were obtained by LiBr-H2O,whereas (60.9% and 19.6%) were obtained from LiNO3-H2O refrigerant.
In the current situation, ranking a general fuzzy number is a difficult task, and variousranking methods have been developed, but no perfect ranking method exists. To solve fullyfuzzy linear programming problems, many ranking functions have been developed andimplemented in the literature. However, all of these methods have some limitations. In thischapter, we propose a new method for comparing two triangular fuzzy numbers in a generalisedform. The Ezzati method [1] has been expanded upon using the suggested approach to handlefully fuzzy linear programming issues (FFLPP). The implementation of the developedalgorithm has been illustrated through numerical illustrations. The proposed algorithm has beenapplied to a transportation problem in light of extensive testing, and it has been discovered thatit is effective and generally offers a better solution.
This research article establishes anti-synchronization between the three-dimensionalnon-identical nonlinear Chen-Lee, Lorenz-Stenflo and Liu-Chen chaotic systems via activenonlinear control techniques. Phase portraits of master and slave systems in the form of antisynchronization are investigated. The stability results are discussed by the stability theory ofLyapunov function. Anti-synchronization of chaotic Chen-Lee system and chaotic Lorenzstenflo systems as well as anti-synchronization of chaotic Chen-Lee and Liu-Chen systems havebeen established using active control methodologies. The active control method is moreefficient to obtain the anti-synchronization between different chaotic systems. Numericalresults are also discussed by the proposed method.
Recently, many soft computing methods have been implemented to extractinformation from big data. A standardized format for evaluating the expression levels ofthousands of genes is made available by DNA microarray technology. Cancers of severalanatomical regions can be identified with the help of patterns developed by gene expressionsin microarray technology. Since the microarray data is too huge to process due to the curse ofdimensionality problem.
Methodology: Therefore, in this chapter, a setup based on a hybrid machine learningframework using soft computing techniques for feature selection is designed and executed toeliminate unnecessary genes and identify important genes for the identification of cancer. Inthe first stage, the genes or the features are taken out with the aid of the higher-orderIndependent Component Analysis (ICA) technique. Then, a wrapper algorithm that is based onSpider Monkey Optimization (SMO) with Genetic Algorithm (GA) is used to find the set ofgenes that improve the classification accuracy of Nave Bayes (NB) classifiers and SupportVector Machine (SVM). For comparison purposes, three other optimization techniquesconsidered in this chapter are Particle Swarm Optimization (PSO), Artificial Bee Colony(ABC), and Genetic Algorithm (GA). After the selection of relevant expressed genes, the mostpopular classifiers namely Nave Bayes (NB) and Support Vector Machine (SVM)) are trainedwith selected genes, and in the end, the accuracy of classification is determined using test data.
Result: The experimental results with five benchmark microarray datasets of cancer prove thatGenetic Spider Monkey (GSM) is a more efficient approach to improve the classificationperformance with ICA for both classifiers.
This work focuses on tie-breaking procedures that employ the fuzzy technique fororder performance by similarity to the ideal solution. A tie situation occurs when two or morecompetitors receive the same score in a competition. Fuzzy technique for order performance bysimilarity to ideal solution provides efficient and effective decision making. Thefuzzy technique for order performance by similarity to ideal solution assesses accurate andsystematic decision-making based on multiple criteria among a finite set of possiblealternatives. The proposed tie-breaking approach establishes an ordering relationship and aranking among a set of alternatives under certain objective and subjective decision criteria. Anumerical example is considered to demonstrate the computing process.
The book's objective is two-fold: (1) It examines the mathematical governing principles of simulation-based optimization, thereby providing the reader with the ability to model relevant real-life problems using these techniques. (2) It outlines the computational technology underlying these methods. Taken together these two aspects demonstrate that the mathematical and computational methods discussed in this book do work.
Broadly speaking, the book has two parts: (1) parametric (static) optimization and (2) control (dynamic) optimization. Some of the book's special features are:
*An accessible introduction to reinforcement learning and parametric-optimization techniques.
*A step-by-step description of several algorithms of simulation-based optimization.
*A clear and simple introduction tothe methodology of neural networks.
*A gentle introduction to convergence analysis of some of the methods enumerated above.
*Computer programs for many algorithms of simulation-based optimization.