The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call theI&Dframe, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are — To the best of our knowledge — Particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems. Finally, the authors discuss open questions and propose an agenda for future work.

Artificial intelligence has made tremendous advances since its inception about seventy years ago. Self-driving cars, programs beating experts at complex games, and smart robots capable of assisting people that need care are just some among the successful examples of machine intelligence. This kind of progress might entice us to envision a society populated by autonomous robots capable of performing the same tasks humans do in the near future. This prospect seems limited only by the power and complexity of current computational devices, which is improving fast. However, there are several significant obstacles on this path. General intelligence involves situational reasoning, taking perspectives, choosing goals, and an ability to deal with ambiguous information. We observe that all of these characteristics are connected to the ability of identifying and exploiting new affordances—opportunities (or impediments) on the path of an agent to achieve its goals. A general example of an affordance is the use of an object in the hands of an agent. We show that it is impossible to predefine a list of such uses. Therefore, they cannot be treated algorithmically. This means that “AI agents” and organisms differ in their ability to leverage new affordances. Only organisms can do this. This implies that true AGI is not achievable in the current algorithmic frame of AI research. It also has important consequences for the theory of evolution. We argue that organismic agency is strictly required for truly open-ended evolution through radical emergence. We discuss the diverse ramifications of this argument, not only in AI research and evolution, but also for the philosophy of science.

Since Newton, classical and quantum physics depend upon the ‘Newtonian paradigm’. The relevant variables of the system are identified. For example, we identify the position and momentum of classical particles. Laws of motion in differential form connecting the variables are formulated. An example is Newton’s three laws of motion. The boundary conditions creating the phase space of all possible values of the variables are defined. Then, given any initial condition, the differential equations of motion are integrated to yield an entailed trajectory in the prestated phase space. It is fundamental to the Newtonian paradigm that the set of possibilities that constitute the phase space is always definable and fixed ahead of time. This fails for the diachronic evolution of ever-new adaptations in any biosphere. Living cells achieve constraint closure and construct themselves. Thus, living cells, evolving via heritable variation and natural selection, adaptively construct new-in-the-universe possibilities. We can neither define nor deduce the evolving phase space: we can use no mathematics based on set theory to do so. We cannot write or solve differential equations for the diachronic evolution of ever-new adaptations in a biosphere. Evolving biospheres are outside the Newtonian paradigm. There can be no theory of everything that entails all that comes to exist. We face a third major transition in science beyond the Pythagorean dream that ‘all is number’ echoed by Newtonian physics. However, we begin to understand the emergent creativity of an evolving biosphere: emergence is not engineering.