List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

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Evolutionary algorithms for solving multi-objective problems

From the Publisher:
Pattern recognition has long been studied in relation to many different (and mainly unrelated) applications, such as remote sensing, computer vision, space research, and medical imaging. In this book Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks. Unifying principles are brought to the fore, and the author gives an overview of the state of the subject. Many examples are included to illustrate real problems in pattern recognition and how to overcome them.This is a self-contained account, ideal both as an introduction for non-specialists readers, and also as a handbook for the more expert reader.

Pattern recognition and neural networks

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

/pdf/computational-complexity-a-modern-approach-5gtk8urev9.pdf

Computational Complexity: A Modern Approach

Information Theory and Reliable Communication

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

In this seminal paper on probabilistic Turing machines, Gill asked whether the class PP is closed under intersection and union. We give a positive answer to this question. We also show that PP is closed under a variety of polynomial-time truth-table reductions. Consequences in complexity theory include the definite collapse and (assuming P ? PP) separation of certain query hierarchies over PP. Similar techniques allow us to combine several threshold gates into a single threshold gate. Consequences in the study of circuits include the simulation of circuits with a small number of threshold gates by circuits having only a single threshold gate at the root (perceptrons) and a lower bound on the number of threshold gates that are needed to compute the parity function.

PP is closed under intersection

The basic techniques for using polynomials in complexity theory are examined, emphasizing intuition at the expense of formality. The focus is on the connections to constant-depth circuits, at the expense of polynomial-time Turing machines. The closure properties, upper bounds, and lower bounds obtained by this approach are surveyed. >

The polynomial method in circuit complexity

AbstractWe show that every languageL in the class ACC can be recognized by depth-two deterministic circuits with a symmetric-function gate at the root and
$$2^{\log ^{O(1)} n} $$
 AND gates of fan-in logO(1)n at the leaves, or equivalently, there exist polynomialspn(x1,..., xn) overZ of degree logO(1)n and with coefficients of magnitude
$$2^{\log ^{O(1)} n} $$
 and functionshn:Z→{0,1} such that for eachn and eachx∈{0,1}n,XL(x)=hn(pn(x1,...,xn)). This improves an earlier result of Yao (1985). We also analyze and improve modulus-amplifying polynomials constructed by Toda (1991) and Yao (1985).

On ACC

We consider the problem of approximating a Boolean functionf∶{0,1}
 n
 →{0,1} by the sign of an integer polynomialp of degreek. For us, a polynomialp(x) predicts the value off(x) if, wheneverp(x)≥0,f(x)=1, and wheneverp(x)<0,f(x)=0. A low-degree polynomialp is a good approximator forf if it predictsf at almost all points. Given a positive integerk, and a Boolean functionf, we ask, “how good is the best degreek approximation tof?” We introduce a new lower bound technique which applies to any Boolean function. We show that the lower bound technique yields tight bounds in the casef is parity. Minsky and Papert [10] proved that a perceptron cannot compute parity; our bounds indicate exactly how well a perceptron canapproximate it. As a consequence, we are able to give the first correct proof that, for a random oracleA, PP
 A
 is properly contained in PSPACE
 A
 . We are also able to prove the old AC0 exponential-size lower bounds in a new way. This allows us to prove the new result that an AC0 circuit with one majority gate cannot approximate parity. Our proof depends only on basic properties of integer polynomials.

The expressive power of voting polynomials

This paper introduces OC1, a new algorithm for generating multivariate decision trees. Multivariate trees classify examples by testing linear combinations of the features at each non-leaf node of the tree. Each test is equivalent to a hyperplane at an oblique orientation to the axes. Because of the computational intractability of finding an optimal orientation for these hyperplanes, heurist.ic methods must be used to produce good trees. This paper explores a new method that combines deterministic and randomized procedures to search for a good tree. Experiments on several different real-world data sets demonstrate that the method consistently finds much smaller trees than comparable methods using univariate tests. In addition, the accuracy of the trees found with our method matches or exceeds the best results of other machine learning methods.

Richard Beigel

Papers

PP is closed under intersection

The polynomial method in circuit complexity

On ACC

The expressive power of voting polynomials

OC1: randomized induction of oblique decision trees