Heuristic

Abstract: In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.

Abstract: Fast and frugal heuristics - simple rules for making decisions with realistic mental resources - are presented here. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? What heuristics are in the mind's adaptive toolbox, and what building blocks compose them? Can judgments based simply on a single reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? This book explores these questions by developing computational models of heuristics and testing them through experiments and analysis. It shows how fast and frugal heuristics can yield adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop-out rates, and playing the stock market.

Abstract: In recent years, various heuristic optimization methods have been developed. Many of these methods are inspired by swarm behaviors in nature. In this paper, a new optimization algorithm based on the law of gravity and mass interactions is introduced. In the proposed algorithm, the searcher agents are a collection of masses which interact with each other based on the Newtonian gravity and the laws of motion. The proposed method has been compared with some well-known heuristic search methods. The obtained results confirm the high performance of the proposed method in solving various nonlinear functions.

Abstract: The Vehicle Routing Problem covers both exact and heuristic methods developed for the VRP and some of its main variants, emphasizing the practical issues common to VRP. The book is composed of three parts containing contributions from well-known experts. The first part covers basic VRP, known more commonly as capacitated VRP. The second part covers three main variants of VRP with time windows, backhauls, and pickup and delivery. The third part covers issues arising in real-world VRP applications and includes both case studies and references to software packages. The book will be of interest to both researchers and graduate-level students in the communities of operations research and matematical sciences. It focuses on a specific family of problems while offering a complete overview of the effective use of the most important techniques proposed for the solution of hard combinatorial problems. Practitioners will find this book particularly usef

Abstract: An iterative mincut heuristic for partitioning networks is presented whose worst case computation time, per pass, grows linearly with the size of the network. In practice, only a very small number of passes are typically needed, leading to a fast approximation algorithm for mincut partitioning. To deal with cells of various sizes, the algorithm progresses by moving one cell at a time between the blocks of the partition while maintaining a desired balance based on the size of the blocks rather than the number of cells per block. Efficient data structures are used to avoid unnecessary searching for the best cell to move and to minimize unnecessary updating of cells affected by each move.