A hybridised evolutionary algorithm for multi-criterion minimum spanning tree problems

A hybridised and Knowledge-based Evolutionary Algorithm (KEA) is applied to the multi-criterion minimum spanning tree problems. Hybridisation is used across its three phases. In the first phase a deterministic single objective optimization algorithm finds the extreme points of the Pareto front. In the second phase a K-best approach finds the first neighbours of the extreme points, which serve as an elitist parent population to an evolutionary algorithm in the third phase. A knowledge-based mutation operator is applied in each generation to reproduce individuals that are at least as good as the unique parent. The advantages of KEA over previous algorithms include its speed (making it applicable to large real-world problems), its scalability to more than two criteria, and its ability to find both the supported and unsupported optimal solutions.

Landscape state machines: Tools for evolutionary algorithm performance analyses and landscape/algorithm mapping

Many evolutionary algorithm applications involve either fitness functions with high time complexity or large dimensionality (hence very many fitness evaluations will typically be needed) or both. In such circumstances, there is a dire need to tune various features of the algorithm well so that performance and time savings are optimized. However, these are precisely the circumstances in which prior tuning is very costly in time and resources. There is hence a need for methods which enable fast prior tuning in such cases. We describe a candidate technique for this purpose, in which we model a landscape as a finite state machine, inferred from preliminary sampling runs. In prior algorithm-tuning trials, we can replace the 'real' landscape with the model, enabling extremely fast tuning, saving far more time than was required to infer the model. Preliminary results indicate much promise, though much work needs to be done to establish various aspects of the conditions under which it can be most beneficially used. A main limitation of the method as described here is a restriction to mutation-only algorithms, but there are various ways to address this and other limitations.

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers' generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Variable selection for financial distress classification using a genetic algorithm

This paper is concerned with the use of a genetic algorithm to select financial ratios for corporate distress classification models. For this purpose, the fitness value associated to a set of ratios is made to reflect the requirements of maximizing the amount of information available for the model and minimizing the collinearity between the model inputs. A case study involving 60 failed and continuing British firms in the period 1997-2000 is used for illustration. The classification model based on ratios selected by the genetic algorithm compares favorably with a model employing ratios usually found in the financial distress literature.

Efficiency of evolutionary algorithms in water network pipe sizing

The pipe sizing of water networks via evolutionary algorithms is of great interest because it allows the selection of alternative economical solutions that meet a set of design requirements. However, available evolutionary methods are numerous, and methodologies to compare the performance of these methods beyond obtaining a minimal solution for a given problem are currently lacking. A methodology to compare algorithms based on an efficiency rate (E) is presented here and applied to the pipe-sizing problem of four medium-sized benchmark networks (Hanoi, New York Tunnel, GoYang and R-9 Joao Pessoa). E numerically determines the performance of a given algorithm while also considering the quality of the obtained solution and the required computational effort. From the wide range of available evolutionary algorithms, four algorithms were selected to implement the methodology: a PseudoGenetic Algorithm (PGA), Particle Swarm Optimization (PSO), a Harmony Search and a modified Shuffled Frog Leaping Algorithm (SFLA). After more than 500,000 simulations, a statistical analysis was performed based on the specific parameters each algorithm requires to operate, and finally, E was analyzed for each network and algorithm. The efficiency measure indicated that PGA is the most efficient algorithm for problems of greater complexity and that HS is the most efficient algorithm for less complex problems. However, the main contribution of this work is that the proposed efficiency ratio provides a neutral strategy to compare optimization algorithms and may be useful in the future to select the most appropriate algorithm for different types of optimization problems.