Explaining Adaptation in Genetic Algorithms With Uniform Crossover: The Hyperclimbing Hypothesis

The hyperclimbing hypothesis is a hypothetical explanation for adaptation in genetic algorithms with uniform crossover (UGAs). Hyperclimbing is an intuitive, general-purpose, non-local search heuristic applicable to discrete product spaces with rugged or stochastic cost functions. The strength of this heuristic lie in its insusceptibility to local optima when the cost function is deterministic, and its tolerance for noise when the cost function is stochastic. Hyperclimbing works by decimating a search space, i.e. by iteratively fixing the values of small numbers of variables. The hyperclimbing hypothesis holds that UGAs work by implementing efficient hyperclimbing. Proof of concept for this hypothesis comes from the use of a novel analytic technique involving the exploitation of algorithmic symmetry. We have also obtained experimental results that show that a simple tweak inspired by the hyperclimbing hypothesis dramatically improves the performance of a UGA on large, random instances of MAX-3SAT and the Sherrington Kirkpatrick Spin Glasses problem.Comment: 22 pages, 5 figure

A parallel multi-population biased random-key genetic algorithm for electric distribution network reconfiguration

This work presents a multi-population biased random-key genetic algorithm (BRKGA) for the electric distribution network reconfiguration problem (DNR). DNR belongs to the class of network design problems which include transportation problems, computer network restoration and telecommunication network design and can be used for loss minimization and load balancing, being an important tool for distribution network operators. A BRKGA is a class of genetic algorithms in which solutions are encoded as vectors of random keys, i.e. randomly generated real numbers from a uniform distribution in the interval [0, 1). A vector of random keys is translated into a solution of the optimization problem by a decoder. The decoder used generates only feasible solutions by using an efficient codification based upon the fundamentals of graph theory, restricting the search space. The parallelization is based on the single program multiple data paradigm and is executed on the cores of a multi-core processor. Time to target plots, which characterize the running times of stochastic algorithms for combinatorial optimization, are used to compare the performance of the serial and parallel algorithms. The proposed method has been tested on two standard distribution systems and the results show the effectiveness and performance of the parallel algorithm

Implementation of Genetic Algorithms in FPGA-based Reconfigurable Computing Systems

Genetic Algorithms (GAs) are used to solve many optimization problems in science and engineering. GA is a heuristics approach which relies largely on random numbers to determine the approximate solution of an optimization problem. We use the Mersenne Twister Algorithm (MTA) to generate a non-overlapping sequence of random numbers with a period of 219937-1. The random numbers are generated from a state vector that consists of 624 elements. Our work on state vector generation and the GA implementation targets the solution of a flow-line scheduling problem where the flow-lines have jobs to process and the goal is to find a suitable completion time for all jobs using a GA. The state vector generation algorithm (MTA) performs poorly in traditional von Neumann architectures due to its poor temporal and spatial locality. Therefore its performance is limited by the speed at which we can access memory. With an approximate increase of processor performance by 60% per year and a drop of memory latency only 7% per year, a new approach is needed for performance improvement. On the other hand, the GA implementation in a general-purpose microprocessor, though performs reasonably well, has scope for performance gain in a parallel implementation. The parallel implementation of the GA can work as a kernel for applications that uses a GA to reach a solution. Our approach is to implement the state vector generation process and the GA in an FPGA-based Reconfigurable Computing (RC) system with the goal of improving the overall performance. Application design for FPGA-based RC systems is not trivial and the performance improvement is not guaranteed. Designing for RC systems requires algorithmic parallelism in order to exploit the inherent parallelism of the FPGA. We are using a high-level language that provides a level of abstraction from the lower-level hardware in the RC system making it difficult to fully exploit some of the architectural benefits of the FPGA. Considering these factors, we improve the state vector generation process algorithmically. Our implementation generates state vectors 5X faster than the previous implementation in an Intel Xeon microprocessor of 2GHz. The modified algorithm is also implemented in a Xilinx Virtex-4 FPGA that results in a 2.4X speedup. Improvement in this preprocessing step accelerates GA application performance as random numbers are generated from these state vectors for the genetic operators. We simulate the basic operations of a GA in an FPGA to study its behavior in a parallel environment and analyze the results. The initial FPGA implementation of the GA runs about 7X slower than its microprocessor counterpart. The reasons are explained along with suggestions for improvement and future work

Black box search : framework and methods

A theoretical framework is constructed to analyze the behavior of all determin-istic non-repeating search algorithms as they apply to all possible functions of a given finite domain and range. A population table data structure is introduced for this purpose, and many properties of the framework are discovered, including the number of deterministic non-repeating search algorithms. Canonical forms are pre-sented for all elements of the framework, as well as methods for converting between the objects and their canonical numbers and back again. The theorems regarding population tables allow for a simple, alternate form of the No Free Lunch (NFL) theorem, an important theorem regarding search algorithm performance over all functions. Previously, this theorem has only been proven in overly-complicated, confusing fashion. Other statements of the NFL theorem are shown in the light of this framework and the theorem is extended to non-complete sets of functions and to a non-trivial definition of stochastic search. The framework allows for an extensive study of minimax distinctions between search algorithms. A change of representation is easily expressed in the framework with obvious performance im-plications. The expected performance of random search with replacement, random search without replacement, and enumeration will be studied in some detail. Claims in the field regarding search algorithm robustness will be tested empirically. Experiments were performed to determine how the compressibility of a function impacts its performance, with an emphasis on randomly selected functions. A genetic algorithm was run on two sets of functions: one set contained functions that were known to be compressible, and the other contained functions that had a high probability of being incompressible. Performance was found to be the same for both sets

A niching memetic algorithm for simultaneous clustering and feature selection

Clustering is inherently a difficult task, and is made even more difficult when the selection of relevant features is also an issue. In this paper we propose an approach for simultaneous clustering and feature selection using a niching memetic algorithm. Our approach (which we call NMA_CFS) makes feature selection an integral part of the global clustering search procedure and attempts to overcome the problem of identifying less promising locally optimal solutions in both clustering and feature selection, without making any a priori assumption about the number of clusters. Within the NMA_CFS procedure, a variable composite representation is devised to encode both feature selection and cluster centers with different numbers of clusters. Further, local search operations are introduced to refine feature selection and cluster centers encoded in the chromosomes. Finally, a niching method is integrated to preserve the population diversity and prevent premature convergence. In an experimental evaluation we demonstrate the effectiveness of the proposed approach and compare it with other related approaches, using both synthetic and real data

A general framework of multi-population methods with clustering in undetectable dynamic environments

Copyright @ 2011 IEEETo solve dynamic optimization problems, multiple population methods are used to enhance the population diversity for an algorithm with the aim of maintaining multiple populations in different sub-areas in the fitness landscape. Many experimental studies have shown that locating and tracking multiple relatively good optima rather than a single global optimum is an effective idea in dynamic environments. However, several challenges need to be addressed when multi-population methods are applied, e.g., how to create multiple populations, how to maintain them in different sub-areas, and how to deal with the situation where changes can not be detected or predicted. To address these issues, this paper investigates a hierarchical clustering method to locate and track multiple optima for dynamic optimization problems. To deal with undetectable dynamic environments, this paper applies the random immigrants method without change detection based on a mechanism that can automatically reduce redundant individuals in the search space throughout the run. These methods are implemented into several research areas, including particle swarm optimization, genetic algorithm, and differential evolution. An experimental study is conducted based on the moving peaks benchmark to test the performance with several other algorithms from the literature. The experimental results show the efficiency of the clustering method for locating and tracking multiple optima in comparison with other algorithms based on multi-population methods on the moving peaks benchmark

Cost-Sensitive Classification: Empirical Evaluation of a Hybrid Genetic Decision Tree Induction Algorithm

This paper introduces ICET, a new algorithm for cost-sensitive classification. ICET uses a genetic algorithm to evolve a population of biases for a decision tree induction algorithm. The fitness function of the genetic algorithm is the average cost of classification when using the decision tree, including both the costs of tests (features, measurements) and the costs of classification errors. ICET is compared here with three other algorithms for cost-sensitive classification - EG2, CS-ID3, and IDX - and also with C4.5, which classifies without regard to cost. The five algorithms are evaluated empirically on five real-world medical datasets. Three sets of experiments are performed. The first set examines the baseline performance of the five algorithms on the five datasets and establishes that ICET performs significantly better than its competitors. The second set tests the robustness of ICET under a variety of conditions and shows that ICET maintains its advantage. The third set looks at ICET's search in bias space and discovers a way to improve the search.Comment: See http://www.jair.org/ for any accompanying file

Understanding Algorithm Performance on an Oversubscribed Scheduling Application

The best performing algorithms for a particular oversubscribed scheduling application, Air Force Satellite Control Network (AFSCN) scheduling, appear to have little in common. Yet, through careful experimentation and modeling of performance in real problem instances, we can relate characteristics of the best algorithms to characteristics of the application. In particular, we find that plateaus dominate the search spaces (thus favoring algorithms that make larger changes to solutions) and that some randomization in exploration is critical to good performance (due to the lack of gradient information on the plateaus). Based on our explanations of algorithm performance, we develop a new algorithm that combines characteristics of the best performers; the new algorithms performance is better than the previous best. We show how hypothesis driven experimentation and search modeling can both explain algorithm performance and motivate the design of a new algorithm