Edges of Mutually Non-dominating Sets

Copyright © 2013 ACM. This is the accepted, peer-reviewed version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Proceedings of the 15th annual conference on Genetic and Evolutionary Computation (GECCO ’13), pp. 607-614, http://dx.doi.org/10.1145/2463372.246345215th annual conference on Genetic and Evolutionary Computation (GECCO ’13), Amsterdam, The Netherlands, 6-10 July 2013Notes: Won the Best Paper Award in the EMO trackMulti-objective optimisation yields an estimated Pareto front of mutually non-dominating solutions, but with more than three objectives understanding the relationships between solutions is challenging. Natural solutions to use as landmarks are those lying near to the edges of the mutually non-dominating set. We propose four definitions of edge points for many-objective mutually non-dominating sets and examine the relations between them. The first defines edge points to be those that extend the range of the attainment surface. This is shown to be equivalent to finding points which are not dominated on projection onto subsets of the objectives. If the objectives are to be minimised, a further definition considers points which are not dominated under maximisation when projected onto objective subsets. A final definition looks for edges via alternative projections of the set. We examine the relations between these definitions and their efficacy for synthetic concave- and convex-shaped sets, and on solutions to a prototypical many-objective optimisation problem, showing how they can reveal information about the structure of the estimated Pareto front

Comparing and Combining Lexicase Selection and Novelty Search

Lexicase selection and novelty search, two parent selection methods used in evolutionary computation, emphasize exploring widely in the search space more than traditional methods such as tournament selection. However, lexicase selection is not explicitly driven to select for novelty in the population, and novelty search suffers from lack of direction toward a goal, especially in unconstrained, highly-dimensional spaces. We combine the strengths of lexicase selection and novelty search by creating a novelty score for each test case, and adding those novelty scores to the normal error values used in lexicase selection. We use this new novelty-lexicase selection to solve automatic program synthesis problems, and find it significantly outperforms both novelty search and lexicase selection. Additionally, we find that novelty search has very little success in the problem domain of program synthesis. We explore the effects of each of these methods on population diversity and long-term problem solving performance, and give evidence to support the hypothesis that novelty-lexicase selection resists converging to local optima better than lexicase selection

A Genetic Programming Approach to Designing Convolutional Neural Network Architectures

The convolutional neural network (CNN), which is one of the deep learning models, has seen much success in a variety of computer vision tasks. However, designing CNN architectures still requires expert knowledge and a lot of trial and error. In this paper, we attempt to automatically construct CNN architectures for an image classification task based on Cartesian genetic programming (CGP). In our method, we adopt highly functional modules, such as convolutional blocks and tensor concatenation, as the node functions in CGP. The CNN structure and connectivity represented by the CGP encoding method are optimized to maximize the validation accuracy. To evaluate the proposed method, we constructed a CNN architecture for the image classification task with the CIFAR-10 dataset. The experimental result shows that the proposed method can be used to automatically find the competitive CNN architecture compared with state-of-the-art models.Comment: This is the revised version of the GECCO 2017 paper. The code of our method is available at https://github.com/sg-nm/cgp-cn

Large-scale parallelization of partial evaluations in evolutionary algorithms for real-world problems

The importance and potential of Gray-Box Optimization (GBO) with evolutionary algorithms is becoming increasingly clear lately, both for benchmark and real-world problems. We consider the GBO setting where partial evaluations are possible, meaning that sub-functions of the evaluation function are known and can be exploited to improve optimization efficiency. In this paper, we show that the efficiency of GBO can be greatly improved through large-scale parallelism, exploiting the fact that each evaluation function requires the calculation of a number of independent sub-functions. This is especially interesting for real-world problems where often the majority of the computational effort is spent on the evaluation function. Moreover, we show how the best parallelization technique largely depends on factors including the number of sub-functions and their required computation time, revealing that for different parts of the optimization the best parallelization technique should be selected based on these factors. As an illustration, we show how large-scale parallelization can be applied to optimization of high-dose-rate brachytherapy treatment plans for prostate cancer. We find that use of a modern Graphics Processing Unit (GPU) was the most efficient parallelization technique in all realistic scenari

Acquiring moving skills in robots with evolvable morphologies: Recent results and outlook

© 2017 ACM. We construct and investigate a strongly embodied evolutionary system, where not only the controllers but also the morphologies undergo evolution in an on-line fashion. In these studies, we have been using various types of robot morphologies and controller architectures in combination with several learning algorithms, e.g. evolutionary algorithms, reinforcement learning, simulated annealing, and HyperNEAT. This hands-on experience provides insights and helps us elaborate on interesting research directions for future development

Spatial redistribution of irregularly-spaced Pareto fronts for more intuitive navigation and solution selection

A multi-objective optimization approach is o.en followed by an a posteriori decision-making process, during which the most appropriate solution of the Pareto set is selected by a professional in the .eld. Conventional visualization methods do not correct for Pareto fronts with irregularly-spaced solutions. However, achieving a uniform spread of solutions can make the decision-making process more intuitive when decision tools such as sliders, which represent the preference for each objective, are used. We propose a method that maps anm-dimensional Pareto front to an (m-1)-simplex and spreads out points to achieve a more uniform distribution of these points in the simplex while maintaining the local neighborhood structure of the solutions as much as possible. .is set of points can then more intuitively be navigated due to the more uniform distribution. We test our approach on a set of non-uniformly spaced 3D Pareto fronts of a real-world problem: deformable image registration of medical images. The results of these experiments are visualized as points in a triangle, showing that we indeed achieve a representation of the Pareto front with a near-uniform distribution of points where these are still positioned as expected, i.e., according to their quality in each of the objectives of interest

Differential Evolution with Reversible Linear Transformations

Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this issue: We propose to generate new candidate solutions by utilizing reversible linear transformations applied to a triplet of solutions from the population. In other words, the population is enlarged by using newly generated individuals without evaluating their fitness. We assess our methods on three problems: (i) benchmark function optimization, (ii) discovering parameter values of the gene repressilator system, (iii) learning neural networks. The empirical results indicate that the proposed approach outperforms vanilla DE and a version of DE with applying differential mutation three times on all testbeds

Exploiting linkage information in real-valued optimization with the real-valued gene-pool optimal mixing evolutionary algorithm

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) has been shown to be among the state-of-the-art for solving discrete optimization problems. Key to the success of GOMEA is its ability to efficiently exploit the linkage structure of a problem. Here, we introduce the Real-Valued GOMEA (RV-GOMEA), which incorporates several aspects of the real-valued EDA known as AMaLGaM into GOMEA in order to make GOMEA well-suited for real-valued optimization. The key strength of GOMEA to competently exploit linkage structure is effectively preserved in RV-GOMEA, enabling excellent performance on problems that exhibit a linkage structure that is to some degree decomposable. Moreover, the main variation operator of GOMEA enables substantial improvements in performance if the problem allows for partial evaluations, which may be very well possible in many real-world applications. Comparisons of performance with state-of-the-art algorithms such as CMA-ES and AMaLGaM on a set of well-known benchmark problems show that RV-GOMEA achieves comparable, excellent scalability in case of black-box optimization. Moreover, RV-GOMEA achieves unprecedented scalability on problems that allow for partial evaluations, reaching near-optimal solutions for problems with up to millions of real-valued variables within one hour on a normal desktop computer