The insights and benefits to be realised through the optimisation of multiple independent, but conflicting objectives are well recognised by practitioners seeking effective and robust solutions to real-world application problems. Key issues encountered by users of many-objective optimisation (>3 objectives) in a real-world environment are discussed here. These include how to formulate the problem and develop a suitable decision-making framework, together with considering different ways in which decision-makers may be involved. Ways to manage the reduction of computational load and how to reduce the sensitivity of candidate solutions as a result of the inevitable uncertainties that arise in real-world applications are addressed. Other state-of-the-art topics such as the use of machine learning and the management of complex issues arising from multidisciplinary applications are also examined. It is recognised that optimisation in real-world applications is commonly undertaken by users and decision-makers who need not have specialist expertise in many-objective optimisation decision analysis methods. Advice is offered to experts and non-experts alike.

The evaluation and analysis of optimisation algorithms through benchmarks is an important aspect of research in evolutionary computation. This is especially true in the context of many-objective optimisation, where the complexity of the problems usually makes theoretical analysis difficult. However, the availability of suitable benchmarking problems is lacking in many research areas within the field of evolutionary computation for example, optimisation under noise or with constraints. Several additional open issues in common benchmarking practice exist as well, for instance related to reproducibility and the interpretation of results. In this book chapter, we focus on discussing these issues for multi- and many-objective optimisation (MMO) specifically. We thus first provide an overview of existing MMO benchmarks and find that besides lacking in number and diversity, improvements are needed in terms of ease of use and the ability to characterise and describe benchmarking functions. In addition, we provide a concise list of common pitfalls to look out for when using benchmarks, along with suggestions of how to avoid them. This part of the chapter is intended as a guide to help improve the usability of benchmarking results in the future.

Many-objective optimization problems (MaOPs) are problems that feature four or more objectives, criteria or attributes that must be considered simultaneously. MaOPs often arise in real-world situations and the development of algorithms for solving MaOPs has become one of the hot topics in the field of evolutionary multi-criteria optimization (EMO). However, much of this energy devoted to MaOP research is arguably detached from the challenges of, and decision analysis requirements for, MaOPs. Motivated by this gap, the authors of this chapter organized a Lorentz Center workshop in 2019 entitled Many-Criteria Optimization and Decision Analysis—MACODA—bringing researchers and practitioners together to reflect on the challenges in many-objective optimization and analysis, and to develop a vision for the next decade of MACODA research. From the workshop arose the MACODA book, for which this chapter forms the introduction. The chapter describes the organizers’ perspectives on the challenges of MaOP. It introduces the history of MaOP principally from the perspective of EMO, from where the terminology originated, but drawing important connections to pre-existing work in the field of multi-criteria decision-making (MCDM) which was the source or inspiration for many EMO ideas. The chapter then offers a brief review of the present state of MACODA research, covering major algorithms, scalarization approaches, objective-space reduction, order extensions to Pareto dominance, preference elicitation, wider decision-maker interaction methods and visualization. In drawing together the vision for MACODA in 2030, the chapter provides synopses of the unique and varied contributions that comprise the MACODA book and identifies further under-explored topics worthy of consideration by researchers over the next decade and beyond.

In multi-objective optimisation, it is common to transform the multi-objective optimisation problem into a (sequence of) single-objective problems, and then compute or approximate the solution(s) of these transformed problems. Scalarisation methods are one such example where a set of solutions is determined by solving a sequence of single-objective problems. Another example are indicator-based methods where the aim is to determine, at once, a set of solutions that maximises a given set-quality indicator, i.e., a single-objective function. The aim of this chapter is to explore the connections between set-quality indicators and scalarisations, and discuss the corresponding theoretical properties. In particular, the connection between the optimal solutions of the original multi-objective problem and the optimal solutions of the single-objective problems into which it is transformed is considered.

Optimisation algorithms are commonly compared on benchmarks to get insight into performance differences. However, it is not clear how closely benchmarks match the properties of real-world problems because these properties are largely unknown. This work investigates the properties of real-world problems through a questionnaire to enable the design of future benchmark problems that more closely resemble those found in the real world. The results, while not representative as they are based on only 45 responses, indicate that many problems possess at least one of the following properties: they are constrained, deterministic, have only continuous variables, require substantial computation times for both the objectives and the constraints, or allow a limited number of evaluations. Properties like known optimal solutions and analytical gradients are rarely available, limiting the options in guiding the optimisation process. These are all important aspects to consider when designing realistic benchmark problems. At the same time, the design of realistic benchmarks is difficult, because objective functions are often reported to be black-box and many problem properties are unknown. To further improve the understanding of real-world problems, readers working on a real-world optimisation problem are encouraged to fill out the questionnaire: https://tinyurl.com/opt-survey .

Chapter 4 presents a model for multi-cellular development by evolving the genetic network that controls the cellular growth process. The central point in this process is to make sure that the evolved gene regulatory network can generate a stable growth process that is able to achieve a balance between cell division and cell apoptosis. It is shown that a self-stabilized growth process can be successfully evolved, which also exhibits self-healing capability after part of the cells in the evolved body is removed. The properties of the gene regulatory network that can lead to a stable growth process are analyzed.

This chapter focuses on evolving the regulatory dynamics most commonly seen in nature. At first, an evolutionary algorithm is adopted to evolve the parameters of a gene regulatory network to generate genetic switches and oscillators. Then, the regulatory logic that combines different regulatory pathways is evolved to synthesize widely seen gene motifs. A step further is to evolve toggle switches and stable oscillators by evolving not only the parameters, but also the regulatory relationships. The evolvability and robustness of the evolved regulatory motifs are examined. Finally, the evolutionary coupling of basic genetic motifs, for instance, the combination of a toggle switch and an oscillator are studied. This chapter is concluded with a real-world example in which a biological gene regulatory pathway governing the production of antibiotics in streptomyces is reconstructed based on gene expression data. This example demonstrates that evolutionary algorithms are competitive in reverse-engineered biological networks containing over 900 genes.

This chapter investigates the synergies between the evolution and development of the nervous systems and the body plan. It starts with the evolution of an undulatory swimming behavior of an elongated animat when the motor configuration and the neural controller are subject to evolution. Then, it is shown that there is a close coupling between the function and complexity of the neural controller and the body plan when the degree of the body plan is under different constraints. Based on this, the development of the body plan is embedded in the model, thus demonstrating a close coupling between the two. Due to the differences in the evolved body plan, different neural controllers emerge, resulting in undulatory and peristaltic locomotive behaviors, respectively. Finally, the development of both the neural controller and the body plan under the regulation of a gene regulatory network is included in the model.

This chapter provides the fundamentals of computational models related to biological evolution and development. It starts with an introduction to evolutionary algorithms for emulating natural evolution in computer systems, including representations, genetic operators, parameter self-adaptation, and their application to single- and multi-objective optimization. This is followed by a presentation of computational models for gene regulatory networks describing the dynamics of the gene expression process, which plays an essential role in biological evolution and development. Then, models for simulating morphological and neural development governed by gene regulatory networks and cellular interactions are given, providing the foundation models for evolving neural and morphological development. Finally, computational models of activity-dependent neural plasticity, including the BCM rule and spike-timing-dependent plasticity rule are given.

This chapter evolves both genetic-driven early neural development and activity-dependent neural plasticity. The evolution of primitive neural development focuses on the evolution of a gene regulatory network that can result in a correct gene expression order reflecting the order of cell division, cell migration, and axon growth using the model animal of hydra. Based on the evolved primitive nervous system consisting of spiking neurons, the hydra-like animat is able to show a food-catching behavior which uses its tentacles to catch food under the control of the evolved nervous system. Then, local activity-dependent neural plasticity rules regulated by a gene regulatory network are evolved to alleviate inference in learning sensory input structure using plasticity in a spiking neural network-based reservoir model. Liquid state machines with self-organized reservoir and multiple sub-reservoir are evolved. Finally, local synaptic and intrinsic rules are evolved to regulate the structure of echo-state-networks for better performing regression and classification tasks.

Based on the evolutionary developmental models presented in the previous chapters, we discuss a possible new approach to artificial general intelligence, which evolves machine learning models that can overcome the limitations of existing deep learning models. It is argued that by taking the evolutionary developmental approach, large models can be evolved and grown in a complex environment, which may equip these models with capabilities of accomplishing multiple tasks, reasoning and planning, and autonomous learning.

This chapter presents various gene-regulated models for self-organizing swarm robots based on a metaphor between multi-cellular morphogenesis and pattern generation of swarm robots. It starts from a simple genetic network model that can generate a predefined pattern to a hierarchical gene regulatory network that can generate patterns that are adaptively generated based on the changing positions of targets to be surrounded. Then, gene regulatory networks that can generate patterns that cover a region rather than the boundary only are presented. Following this, gene regulatory networks that are evolved based on simple motifs are used to generate patterns for swarm robots, thus lifting the requirement to manually define the structure of the hierarchical gene regulatory network. Finally, reaction-diffusion models are adopted for simplistic robots to format patterns and follow moving targets.

Chapter 2 analyzes two key properties of gene regulatory networks, robustness and evolvability, both of which are also quintessential to the evolution of biological systems. After providing a definition of robustness and evolvability, we discuss the relationship between them, and the relationship between the connectivity of gene regulatory networks and their robustness. Then, we evolve the robustness and evolvability of two gene regulatory networks, a Boolean network model and an ordinary differential equation model. The empirical results reveal that there is a hard trade-off between the robustness and evolvability of the Boolean network, which describes a stationary map between the genotype and phenotype. By contrast, a gene regulatory network described by the ordinary differential equation can have both strong robustness and high evolvability, indicating that the developmental plasticity contributes to the ability to have both strong robustness and high evolvability.

AbstractSpatial organization on the atomic scale is one of the key objectives of nanotechnology. The development of DNA nanotechnology is a hallmark of material programmability in 2D and 3D, in which the large variety of available DNA modifications allows it to be interfaced with a number of inorganic and organic materials. Nature’s solution to spatiotemporal control has been the evolution of self-organizing protein systems capable of pattern formation through energy dissipation. Here, we show that combining DNA origami with a minimal micron-scale pattern-forming system vastly expands the applicability of DNA nanotechnology, whether for the development of biocompatible materials or as an essential step toward building synthetic cells from the bottom up. We first describe the interaction of DNA origami nanostructures with model lipid membranes and introduce the self-organizing MinDE protein system from Escherichia coli. We then outline how we used DNA origami to elucidate diffusiophoresis on membranes through MinDE protein pattern formation. We describe how this novel biological transport mechanism can, in turn, be harnessed to pattern DNA origami nanostructures on the micron scale on lipid membranes. Finally, we discuss how our approach could be used to create the next generation of hybrid materials, through cargo delivery and multiscale molecular patterning capabilities.

AbstractDynamic DNA nanotechnology aims at the realization of molecular machines, devices, and dynamic chemical systems using DNA molecules. DNA is used to assemble the components of these systems, define the interactions between the components, and in many cases also as a chemical fuel that drives them using hybridization energy. Except for biosensing, applications of dynamic DNA devices have so far been limited to proof-of-concept demonstrations, partly because the systems are operating rather slowly, and because it is difficult to operate them continuously for extended periods of time. It is argued that one of the major challenges for the future development of dynamic DNA systems is the identification of driving mechanisms that will allow faster and continuous operation far from chemical equilibrium. Such mechanisms will be required to realize active molecular machinery that can perform useful tasks in nanotechnology and molecular robotics.

Multimodality plays a key role as one of the most challenging problem characteristics in the common understanding of solving optimization tasks. Based on insights from the single-objective optimization domain, local optima are considered to be (deceptive) traps for optimization approaches such as gradient descent or different kinds of neighborhood search. Consequently, as continuous multi-objective (MO) problems usually combine multiple (often multimodal) single-objective problems, multimodality is considered an important challenge for MO problems as well. In fact, even very simple MO problems possess a multimodal landscape due to the interactions among its objectives. Thus, modern benchmarks name multimodality an important problem characteristic, while at the same time, heuristic algorithms (like evolutionary algorithms) are expected to be almost mandatory for handling multimodality in an effective way. Here, we continue our previous work by (1) formally defining multimodality in the continuous MO setting, (2) provide techniques for visualizing landscapes of continuous MO problems—not only in the objective but also in the decision space—to improve the intuition regarding continuous MO multimodality, and (3) analyze MO problems based on examples from an extensive test-bed. Thereby, we provide the tools for displaying and detecting basins of attraction, as well as superpositions of local optima, in the decision space of the landscapes. Most important, and maybe unexpected, we are able to show that multimodality in continuous MO optimization differs largely from our understanding of multimodality in the single-objective domain: for simple MO optimization approaches, local efficient sets are often no traps. Instead, locality can even be exploited to slide toward the global efficient set.

Here we describe quality diversity algorithms, a recent and powerful class of evolutionary algorithms that produces a diverse set of high-performing solutions. The optimization paradigm emphasizes phenotypic niching and egalitarian treatment of quality and diversity. We ground quality diversity in ecology, describe the historical development, and give an intuition and formalization of the algorithms. We present a practical example that we refer to for engineers and laymen readers to understand how and why quality diversity can be used. The main insights from research of quality diversity, performance metrics, and benchmarks are discussed. Finally, the open challenges are presented.

An important subtask in multimodal optimization is the identification of the attraction basins of individual optima. The knowledge about these basins can, for example, be used to start an appropriate number of local searches or to classify the problem instance in an exploratory landscape analysis before the optimization is started. In a black-box setting, the identification process necessarily needs a sample of evaluated solutions as input data. As these evaluations are expensive, it would be desirable to reuse previously acquired samples, if existing. In this case, arbitrary mixture distributions of the data must be assumed. Unfortunately, there is no basin identification method currently available that is robust to spatial outliers in the sample and at the same time can provide a ranking and/or a clustering of all the solutions. Topographical selection, which is based on a k-nearest-neighbor graph, is robust against outliers, but does not provide clustering information and determines the number of selected solutions on its own. Nearest-better clustering, on the other hand, can provide a hierarchical clustering but is not very robust to outliers. In this work, we adopt ideas from density-based clustering to develop a new basin identification method. The core idea is to use the number of neighbors within the distance to the nearest-better neighbor as a selection criterion. Experiments show that the new method combines the desirable features of the existing ones.

Many real-world optimization problems are multimodal by nature, and there may exist a large number of optimal solutions. Despite having the same or similar objective values, solutions can still differ in terms of technical feasibility or the preferred range of their decision variable values. Therefore, it is more desirable to employ optimization methods capable of offering several optimal solutions to the Decision Maker (DM). Existing niching methods aim to find all possible solutions in a single optimization run, resulting in possibly too many options to choose from. Due to limited resources available for evaluating solutions in practice, the DM, however, might only be interested in finding a few sufficiently different solutions quickly. This work aims to facilitate this decision-making process by providing only a number of representative solutions to the DM. This way, the DM is not overloaded with superfluous information, resulting in faster and better decision-making. This paper proposes a novel niching method, Suppression Radius-based Niching (SRN), based on the principle of suppression radius to determine representative niching areas. The proposed method is especially appealing for real-world scenarios where reducing the number of function evaluations is crucial due to the high computational costs of evaluations.

The refinement of machine learning strategies and deep convolutional networks led to the development of artificial systems whose functions resemble those of natural brains, suggesting that the two systems share the same computational principles. In this chapter, evidence is reviewed which indicates that the computational operations of natural systems differ in some important aspects from those implemented in artificial systems. Natural processing architectures are characterized by recurrence and therefore exhibit high-dimensional, non-linear dynamics. Moreover, they use learning mechanisms that support self-organization. It is proposed that these properties allow for computations that are notoriously difficult to realize in artificial systems. Experimental evidence on the organization and function of the cerebral cortex is reviewed that supports this proposal.

This chapter provides a comprehensive survey of the researches and motivations for hardware implementation of reservoir computing (RC) on neuromorphic electronic systems. Due to its computational efficiency and the fact that training amounts to a simple linear regression, both spiking and non-spiking implementations of reservoir computing on neuromorphic hardware have been developed. Here, a review of these experimental studies is provided to illustrate the progress in this area and to address the technical challenges which arise from this specific hardware implementation. Moreover, to deal with the challenges of computation on such unconventional substrates, several lines of potential solutions are presented based on advances in other computational approaches in machine learning.

In this chapter, we consider realizing a reservoir computer on an electronic chip that allows for many tens of network nodes whose connection topology can be quickly reconfigured. The reservoir computer displays analog-like behavior and has the potential to perform computations beyond that of a classic Turning machine. In detail, we present our preliminary results of using a physical reservoir computer for performing the task of identifying written digits. The reservoir is realized on a commercially available electronic device known as a field-programmable gate array on which we create an autonomous Boolean network for information processing. Even though the network nodes are Boolean logic elements, they display analog behavior because there is no master clock that controls the nodes. In addition, the electronic signals related to the written-digit images are injected into the reservoir at high speed, leading to the possibility of full-image classification on the nanosecond time scale. We explore the dynamics of the autonomous Boolean networks in response to injected signals and, based on these results, investigate the performance of the reservoir computer on the written-digit task. For a wide range of reservoir structures, we obtain a typical performance of $$\sim $$ 90% for correctly identifying a written digit, which exceeds that obtained by a linear classifier. This work paves the way for achieving low-power, high-speed reservoir computing on readily available field-programmable gate arrays, which are well matched to existing computing infrastructure.

Estimation-of-distribution algorithms (EDAs) are general metaheuristics used in optimization that represent a more recent alternative to classical approaches such as evolutionary algorithms. In a nutshell, EDAs typically do not directly evolve populations of search points but build probabilistic models of promising solutions by repeatedly sampling and selecting points from the underlying search space. Recently, significant progress has been made in the theoretical understanding of EDAs. This chapter provides an up-to-date overview of the most commonly analyzed EDAs and the most recent theoretical results in this area. In particular, emphasis is put on the runtime analysis of simple univariate EDAs, including a description of typical benchmark functions and tools for the analysis. Along the way, open problems and directions for future research are described.

When investigating possible molecular forms for next-generation electronics, the architectures and computing paradigms – either resembling those of classical electronics, or being entirely new - are often established a priori. Research on materials is a subsequent step, which aims to find, in the vast world of molecular materials, those most closely resembling the needed properties. Sometimes, the opposite approach can be both necessary and fruitful. Looking at the characteristics of real-world molecules, and adapting the architecture to them where a tradeoff is possible, is likely a more effective approach than trying to find the right molecule, based on a long list of requirements, often very difficult to fulfil. Here, the problem of matching architecture and materials is introduced, using the promising Quantum-dot Cellular Automata (QCA) paradigm.