/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

http://masou-keshtkar.persiangig.com/document/sdarticle.pdf

GSA: A Gravitational Search Algorithm

An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. It is shown how to take advantage of the form of the limited memory approximation to implement the algorithm efficiently. The results of numerical tests on a set of large problems are reported.

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A limited memory algorithm for bound constrained optimization

A unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, parallel, and distributed metaheuristics Implementing metaheuristics on sequential and parallel machines Using many case studies and treating design and implementation independently, this book gives readers the skills necessary to solve large-scale optimization problems quickly and efficiently. It is a valuable reference for practicing engineers and researchers from diverse areas dealing with optimization or machine learning; and graduate students in computer science, operations research, control, engineering, business and management, and applied mathematics.

/pdf/metaheuristics-from-design-to-implementation-1vqdfv8nk9.pdf

Metaheuristics: From Design to Implementation

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke& Jeeves, implicit filtering, MDS, and Nelder& Mead schemes in a unified way.

/pdf/iterative-methods-for-optimization-4099pll8og.pdf

Iterative Methods for Optimization

This paper contains a bibliography of all references central to bilevel and multilevel programming that the authors know of. It should be regarded as a dynamic and permanent contribution since all the new and appropriate references that are brought to our attention will be periodically added to this bibliography. Readers are invited to suggest such additions, as well as corrections or modifications, and to obtain a copy of the LaTeX and BibTeX files that constitute this manuscript, using the guidelines contained in this paper. To classify some of the references in this bibliography a short overview of past and current research in bilevel and multilevel programming is included. For those who are interested in but unfamiliar with the references in this area, we hope that this bibliography facilitates and encourages their research.

Bilevel and multilevel programming: A bibliography review

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient projection method converges to a nondegenerate point of a linearly constrained problem, then the active and binding constraints are identified in a finite number of iterations. As an application of our theory, we develop quadratic programming algorithms that iteratively explore a subspace defined by the active constraints. These algorithms are able to drop and add many constraints from the active set, and can either compute an accurate minimizer by a direct method, or an approximate minimizer by an iterative method of the conjugate gradient type. Thus, these algorithms are attractive for large scale problems. We show that it is possible to develop a finite terminating quadratic programming algorithm without non-degeneracy assumptions.

Projected gradient methods for linearly constrained problems

This article introduces a multi-objective approach to modeling the urban school bus routing problem and describes an algorithm for generating a solution to this problem. Because school bus transportation services are provided through the public sector, the service must be evaluated by both efficiency and equity measures. The proposed technique first groups students into clusters using a multi-objective districting algorithm and then generates a school bus route and the bus stops for each cluster using a combination of a set covering algorithm and a traveling salesman problem algorithm. Numerical results are reported using test data from Wellington County, Ontario.

A multi-objective optimization approach to urban school bus routing: formulation and solution method

A new transit operating strategy is presented in which service vehicles operate in pairs with the lead vehicle providing an all-stop local service and the following vehicle being allowed to skip some stops as an express service. The underlying scheduling problem is formulated as a nonlinear integer programming problem with the objective of minimizing the total costs for both operators and passengers. A sensitivity analysis using a real-life example is performed to identify the conditions under which the proposed operating strategy is most advantageous.

Paul H. Calamai

Papers

Bilevel and multilevel programming: A bibliography review

Projected gradient methods for linearly constrained problems

A multi-objective optimization approach to urban school bus routing: formulation and solution method

Real-Time Optimization Model for Dynamic Scheduling of Transit Operations

Application of genetic algorithms to the design optimization of an active vehicle suspension system