Covering Tour Problem (CTP) is the generalized form of Traveling Salesman Problem (TSP), which has found different applications in the designing of distribution networks, disaster relief, and transportation routing. The purpose of this problem is to determine the Hamiltoniancyclewiththe lowest costusinga subset of all the nodes, such that the other nodes would be in a distance shorter than the ...

The conjugate gradient method was an efficient technique for solving the unconstrained optimization problem. In this paper, we made a linear combination with parameters β k of the DY method and the HS method, and putted forward the hybrid method of DY and HS. We also proposed the hybrid of FR and PRP by the same mean. Additionally, to present the two hybrid methods, we promoted the Wolfe line s...

Economic dispatch with valve point effect and Prohibited Operating Zones (POZs) is a non-convex and discontinuous optimization problem. Harmony Search (HS) is one of the recently presented meta-heuristic algorithms for solving optimization problems, which has different variants. The performances of these variants are severely affected by selection of different parameters of the algorithm. Intel...

Main methods, algorithms and applications of the Variable Neighborhood Search metaheuristic are surveyed, in view of a chapter of the Encyclopedia of Optimization.

Local search is one of the fundamental paradigms for solving computationally hard combinatorial problems, including the constraint satisfaction problem (CSP). It provides the basis for some of the most successful and versatile methods for solving the large and difficult problem instances encountered in many real-life applications. Despite impressive advances in systematic, complete search algor...

A unified approach to analyzing search algorithms is presented. Each algorithm is characterized by the types of random problems that it can solve rapidly. The results are displayed in a way that clearly indicabes the strengths and weaknesses of each algorithm. Many interesting problems can, at present, best be solved by search methods [7]. In the worst case, searching requires exponent ial time...

Homology search methods have advanced substantially in recent years. Beginning with the elegant Needleman-Wunsch and Smith-Waterman dynamic programming techiques of the 1970s, algorithms have been developed that were appropriate for the data sets and computer systems of their times. As data sets grew, faster but less sensitive heuristic algorithms, such as FASTA and BLAST, became a dominant for...

In this chapter, we review the work of automated geometry theorem proving based on heuristic search methods and report some recent advances in this direction, especially the geometry deductive database which shows surprising power in terms of proving and discovering difficult geometry theorems. We also discuss several key issues in developing an efficient geometry theorem prover with heuristic ...