A central aim of cognitive science is to understand the fundamental mechanisms that enable humans to navigate and make sense of complex environments. In this letter, we argue that computational complexity theory, a foundational framework for evaluating computational resource requirements, holds significant potential in addressing this challenge. As humans possess limited cognitive resources for processing vast amounts of information, understanding how humans perform complex cognitive tasks requires comprehending the underlying factors that drive information processing demands. Computational complexity theory provides a (...) comprehensive theoretical framework to achieve this goal. By adopting this framework, we can gain new insights into how cognitive systems work and develop a more nuanced understanding of the relation between task complexity and human behavior. We provide empirical evidence supporting our argument and identify several open research questions and challenges in applying computational complexity theory to human decision‐making and cognitive science at large. (shrink)

The travelling salesman problem is one of the most popular problems in combinatorial optimization. It has been frequently used as a benchmark of the performance of evolutionary algorithms. For this reason, nowadays practitioners request new and more difficult instances of this problem. This leads to investigate how to evaluate the intrinsic difficulty of the instances and how to separate ease and difficult instances. By developing methodologies for separating easy- from difficult-to-solve instances, researchers can fairly test the performance of their combinatorial (...) optimizers. In this work, a methodology for evaluating the difficulty of instances of the travelling salesman problem near the optimal solution is proposed. The question is if the fitness landscape near the optimal solution encodes enough information to separate instances in function of their intrinsic difficulty. This methodology is based on the use of a random walk to explore the closeness of the optimal solution. The optimal solution is modified by altering one connection between two cities at each step, at the same time that the fitness of the altered solution is evaluated. This permits evaluating the slope of the fitness landscape. Later, and using the previous information, the difficulty of the instance is evaluated with random forests and artificial neural networks. In this work, this methodology is confronted with a wide set of instances. As a consequence, a methodology to separate the instances of the travelling salesman problem by their degree of difficulty is proposed and evaluated. (shrink)