Test Problems for Large-Scale Multiobjective and Many-Objective Optimization.

The interests in multiobjective and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multiobjective and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multiobjective and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms (EAs) for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multiobjective and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multiobjective and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and nonuniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multiobjective and many-objective EAs are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.

Evolution by adapting surrogates.

To deal with complex optimization problems plagued with computationally expensive fitness functions, the use of surrogates to replace the original functions within the evolutionary framework is becoming a common practice. However, the appropriate datacentric approximation methodology to use for the construction of surrogate model would depend largely on the nature of the problem of interest, which varies from fitness landscape and state of the evolutionary search, to the characteristics of search algorithm used. This has given rise to the plethora of surrogate-assisted evolutionary frameworks proposed in the literature with ad hoc approximation/surrogate modeling methodologies considered. Since prior knowledge on the suitability of the data centric approximation methodology to use in surrogate-assisted evolutionary optimization is typically unavailable beforehand, this paper presents a novel evolutionary framework with the evolvability learning of surrogates (EvoLS) operating on multiple diverse approximation methodologies in the search. Further, in contrast to the common use of fitness prediction error as a criterion for the selection of surrogates, the concept of evolvability to indicate the productivity or suitability of an approximation methodology that brings about fitness improvement in the evolutionary search is introduced as the basis for adaptation. The backbone of the proposed EvoLS is a statistical learning scheme to determine the evolvability of each approximation methodology while the search progresses online. For each individual solution, the most productive approximation methodology is inferred, that is, the method with highest evolvability measure. Fitness improving surrogates are subsequently constructed for use within a trust-region enabled local search strategy, leading to the self-configuration of a surrogate-assisted memetic algorithm for solving computationally expensive problems. A numerical study of EvoLS on commonly used benchmark problems and a real-world computationally expensive aerodynamic car rear design problem highlights the efficacy of the proposed EvoLS in attaining reliable, high quality, and efficient performance under a limited computational budget.

Evolution and analysis of genetic networks for stable cellular growth and regeneration.

A computational model is presented that simulates stable growth of cellular structures that are in some cases capable of regeneration. In the model, cellular growth is governed by a gene regulatory network. By evolving the parameters and structure of the genetic network using a modified evolution strategy, a dynamically stable state can be achieved in the developmental process, where cell proliferation and cell apoptosis reach an equilibrium. The results of evolution with different setups in fitness evaluation during the development are compared with respect to their regeneration capability as well as their gene regulatory network structure. Network motifs responsible for stable growth and regeneration that emerged from the evolution are also analyzed. We expect that our findings can help to gain a better understanding of the process of growth and regeneration inspired by biological systems, in order to solve complex engineering problems, such as the design of self-healing materials.

Robustness of glycolysis in yeast to internal and external noise.

Glycolysis is one of the most essential intracellular networks, found in a wide range of organisms. Due to its importance and due to its wide industrial applications, many experimental studies on all details of this process have been performed. Until now, however, to the best of our knowledge, there has been no comprehensive investigation of the robustness of this important process with respect to internal and external noise. To close this gap, we applied two complementary and mutually supporting approaches to a full-scale model of glycolysis in yeast: (a) a linear stability analysis based on a generalized modeling that deals only with those effective parameters of the system that are relevant for its stability, and (b) a numerical integration of the rate equations in the presence of noise, which accounts for imperfect mixing. The results suggest that the occurrence of metabolite oscillations in part of the parameter space is a side effect of the optimization of the system for maintaining a constant adenosine triphosphate level in the face of a varying energy demand and of fluctuations in the parameters and metabolite concentrations.

Vector field embryogeny.

We present a novel approach toward evolving artificial embryogenies, which omits the graph representation of gene regulatory networks and directly shapes the dynamics of a system, i.e., its phase space. We show the feasibility of the approach by evolving cellular differentiation, a basic feature of both biological and artificial development. We demonstrate how a spatial hierarchy formulation can be integrated into the framework and investigate the evolution of a hierarchical system. Finally, we show how the framework allows the investigation of allometry, a biological phenomenon, and its role for evolution. We find that direct evolution of allometric change, i.e., the evolutionary adaptation of the speed of system states on transient trajectories in phase space, is advantageous for a cellular differentiation task.

The influence of learning on evolution: a mathematical framework.

The Baldwin effect can be observed if phenotypic learning influences the evolutionary fitness of individuals, which can in turn accelerate or decelerate evolutionary change. Evidence for both learning-induced acceleration and deceleration can be found in the literature. Although the results for both outcomes were supported by specific mathematical or simulation models, no general predictions have been achieved so far. Here we propose a general framework to predict whether evolution benefits from learning or not. It is formulated in terms of the gain function, which quantifies the proportional change of fitness due to learning depending on the genotype value. With an inductive proof we show that a positive gain-function derivative implies that learning accelerates evolution, and a negative one implies deceleration under the condition that the population is distributed on a monotonic part of the fitness landscape. We show that the gain-function framework explains the results of several specific simulation models. We also use the gain-function framework to shed some light on the results of a recent biological experiment with fruit flies.

Influence of plasticity and learning on evolution under directional selection.

Phenotypic plasticity and related processes (learning, developmental noise) have been proposed to both accelerate and slow down genetically based evolutionary change. While both views have been supported by various mathematical models and simulations, no general predictions have been offered as to when these alternative outcomes should occur. Here we propose a general framework to study the effects of plasticity on the rate of evolution under directional selection. It is formulated in terms of the fitness gain gradient, which measures the effect of a marginal change in the degree of plasticity on the slope of the relationship between the genotypic value of the focal trait and log fitness. If the gain gradient has the same sign as the direction of selection, an increase in plasticity will magnify the response to selection; if the two signs are opposite, greater plasticity will lead to slower response. We use this general result to derive conditions for the acceleration/deceleration under several simple forms of plasticity, including developmental noise. We also show that our approach explains the results of several specific models from the literature and thus provides a unifying framework.

Evolutionary optimization of a hierarchical object recognition model.

A major problem in designing artificial neural networks is the proper choice of the network architecture. Especially for vision networks classifying three-dimensional (3-D) objects this problem is very challenging, as these networks are necessarily large and therefore the search space for defining the needed networks is of a very high dimensionality. This strongly increases the chances of obtaining only suboptimal structures from standard optimization algorithms. We tackle this problem in two ways. First, we use biologically inspired hierarchical vision models to narrow the space of possible architectures and to reduce the dimensionality of the search space. Second, we employ evolutionary optimization techniques to determine optimal features and nonlinearities of the visual hierarchy. Here, we especially focus on higher order complex features in higher hierarchical stages. We compare two different approaches to perform an evolutionary optimization of these features. In the first setting, we directly code the features into the genome. In the second setting, in analogy to an ontogenetical development process, we suggest the new method of an indirect coding of the features via an unsupervised learning process, which is embedded into the evolutionary optimization. In both cases the processing nonlinearities are encoded directly into the genome and are thus subject to optimization. The fitness of the individuals for the evolutionary selection process is computed by measuring the network classification performance on a benchmark image database. Here, we use a nearest-neighbor classification approach, based on the hierarchical feature output. We compare the found solutions with respect to their ability to generalize. We differentiate between a first- and a second-order generalization. The first-order generalization denotes how well the vision system, after evolutionary optimization of the features and nonlinearities using a database A, can classify previously unseen test views of objects from this database A. As second-order generalization, we denote the ability of the vision system to perform classification on a database B using the features and nonlinearities optimized on database A. We show that the direct feature coding approach leads to networks with a better first-order generalization, whereas the second-order generalization is on an equally high level for both direct and indirect coding. We also compare the second-order generalization results with other state-of-the-art recognition systems and show that both approaches lead to optimized recognition systems, which are highly competitive with recent recognition algorithms.