Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessof-fit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the Xie-Beni index and the C-means functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal non-dominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set.Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality

An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles

"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission

An Empirical Study of Cohesion and Coupling: Balancing Optimisation and Disruption

Search based software engineering has been extensively applied to the problem of finding improved modular structures that maximise cohesion and minimise coupling. However, there has, hitherto, been no longitudinal study of developers’ implementations, over a series of sequential releases. Moreover, results validating whether developers respect the fitness functions are scarce, and the potentially disruptive effect of search-based remodularisation is usually overlooked. We present an empirical study of 233 sequential releases of 10 different systems; the largest empirical study reported in the literature so far, and the first longitudinal study. Our results provide evidence that developers do, indeed, respect the fitness functions used to optimise cohesion/coupling (they are statistically significantly better than arbitrary choices with p << 0.01), yet they also leave considerable room for further improvement (cohesion/coupling can be improved by 25% on average). However, we also report that optimising the structure is highly disruptive (on average more than 57% of the structure must change), while our results reveal that developers tend to avoid such disruption. Therefore, we introduce and evaluate a multi-objective evolutionary approach that minimises disruption while maximising cohesion/coupling improvement. This allows developers to balance reticence to disrupt existing modular structure, against their competing need to improve cohesion and coupling. The multi-objective approach is able to find modular structures that improve the cohesion of developers’ implementations by 22.52%, while causing an acceptably low level of disruption (within that already tolerated by developers)

A maximal clique based multiobjective evolutionary algorithm for overlapping community detection

Detecting community structure has become one im-portant technique for studying complex networks. Although many community detection algorithms have been proposed, most of them focus on separated communities, where each node can be-long to only one community. However, in many real-world net-works, communities are often overlapped with each other. De-veloping overlapping community detection algorithms thus be-comes necessary. Along this avenue, this paper proposes a maxi-mal clique based multiobjective evolutionary algorithm for over-lapping community detection. In this algorithm, a new represen-tation scheme based on the introduced maximal-clique graph is presented. Since the maximal-clique graph is defined by using a set of maximal cliques of original graph as nodes and two maximal cliques are allowed to share the same nodes of the original graph, overlap is an intrinsic property of the maximal-clique graph. Attributing to this property, the new representation scheme al-lows multiobjective evolutionary algorithms to handle the over-lapping community detection problem in a way similar to that of the separated community detection, such that the optimization problems are simplified. As a result, the proposed algorithm could detect overlapping community structure with higher partition accuracy and lower computational cost when compared with the existing ones. The experiments on both synthetic and real-world networks validate the effectiveness and efficiency of the proposed algorithm

An evolutionary algorithm with double-level archives for multiobjective optimization

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problemlevel and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed

System optimization by multiobjective genetic algorithms and analysis of the coupling between variables, constraints and objectives

This paper presents a methodology based on Multiobjective Genetic Algorithms (MOGA’s) for the design of electrical engineering systems. MOGA’s allow to optimize multiple heterogeneous criteria in complex systems, but also simplify couplings and sensitivity analysis by determining the evolution of design variables along the Pareto-optimal front. A rather simplified case study dealing with the optimal dimensioning of an inverter – permanent magnet motor – reducer – load association is carried out to demonstrate the interest of the approach

Search based software engineering: Trends, techniques and applications

© ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version is available from the link below.In the past five years there has been a dramatic increase in work on Search-Based Software Engineering (SBSE), an approach to Software Engineering (SE) in which Search-Based Optimization (SBO) algorithms are used to address problems in SE. SBSE has been applied to problems throughout the SE lifecycle, from requirements and project planning to maintenance and reengineering. The approach is attractive because it offers a suite of adaptive automated and semiautomated solutions in situations typified by large complex problem spaces with multiple competing and conflicting objectives. This article provides a review and classification of literature on SBSE. The work identifies research trends and relationships between the techniques applied and the applications to which they have been applied and highlights gaps in the literature and avenues for further research.EPSRC and E