Dynamics of heuristic optimization algorithms on random graphs

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, and some environment of it, is covered and removed from the graph. This graph reduction process can be described as a Markovian dynamics in the space of random graphs of arbitrary degree distribution. We discuss some solvable cases, including algorithms already analysed using different techniques, and develop approximation schemes for more complicated cases. The approximations are corroborated by numerical simulations.Comment: 19 pages, 3 figures, version to app. in EPJ

A COMPARATIVE STUDY OF HEURISTIC OPTIMIZATION ALGORITHMS

Heuristic optimization algorithms are of great importance for reaching solutions to various real world problems. These algorithms have a wide range of applications such as cost reduction, artificial intelligence, and medicine. By the term cost, one could imply that that cost is associated with, for instance, the value of a function of several independent variables. Often, when dealing with engineering problems, we want to minimize the value of a function in order to achieve an optimum, or to maximize another parameter which increases with a decrease in the cost (the value of this function). The heuristic cost reduction algorithms work by finding the optimum values of the independent variables for which the value of the function (the “cost”) is the minimum. There is an abundance of heuristic cost reduction algorithms to choose from. We will start with a discussion of various optimization algorithms such as Memetic algorithms, force-directed placement, and evolution-based algorithms. Following this initial discussion, we will take up the working of three algorithms and implement the same in MATLAB. The focus of this report is to provide detailed information on the working of three different heuristic optimization algorithms, and conclude with a comparative study on the performance of these algorithms when implemented in MATLAB. In this report, the three algorithms we will take in to consideration will be the non-adaptive simulated annealing algorithm, the adaptive simulated annealing algorithm, and random restart hill climbing algorithm. The algorithms are heuristic in nature, that is, the solution these achieve may not be the best of all the solutions but provide a means to reach a quick solution that may be a reasonably good solution without taking an indefinite time to implement

Conditioning of extreme learning machine for noisy data using heuristic optimization

This article provides a tool that can be used in the exact sciences to obtain good approximations to reality when noisy data is inevitable. Two heuristic optimization algorithms are implemented: Simulated Annealing and Particle Swarming for the determination of the extreme learning machine output weights. The first operates in a large search space and at each iteration it probabilistically decides between staying at its current state or moving to another. The swarm of particles, it optimizes a problem from a population of candidate solutions, moving them throughout the search space according to position and speed. The methodology consists of building data sets around a polynomial function, implementing the heuristic algorithms and comparing the errors with the traditional computation method using the Moore–Penrose inverse. The results show that the heuristic optimization algorithms implemented improve the estimation of the output weights when the input have highly noisy data

Adaptive True Proportional Navigation Guidance Based On Heuristic Optimization Algorithms

The PN-guidance (Proportional Guidance) still continues to be improved, because it is the simplest, cheapest and most reliable algorithm. One of the most important techniques to improve PN-guidance is to adapt the navigation constant depending on time. In this study, first, the entire adaptation methods for PN-guidance are classified, then the adaptation process is online achieved by using heuristic optimization during guiding the missile. The novelty of this study is that the heuristic optimization approach is used at the first time to update the navigation constant of PN-guidance. It is considered that having short program code, fast convergence speed and just simple algebraic computations without derivative are vital advantages of heuristic algorithms using into missile systems. In this scope, an Adaptive True-PN (ATPN) guidance algorithm is designed by optimizing navigation constants varying according to the target behavior. The results show that while the acceleration gap of the pitch axis decreases 21.8%, the acceleration gap of yaw axis reduces 39.68%. These reductions mean that while the missile guided by ATPN is maneuvering, it is exposed to less acceleration and less strain. &nbsp