Evolutionary algorithms and ant colony optimisation are used to solve complex real-world problems, but no one fully understands why they work so well. This project builds a mathematical framework to explain the computational power of bio-inspired search heuristics—algorithms that mimic natural processes like evolution or swarm behaviour. Unlike traditional problem-specific methods, these algorithms use a population of candidate solutions that explore many possibilities simultaneously. The research aims to answer fundamental questions: how population size and diversity affect solution quality, how parallel computing can speed up these algorithms, and how genetic programming—where computer programs evolve themselves—can be made reliable and efficient. If successful, the work will create a new classification system for computational problems, clarifying when bio-inspired methods outperform conventional algorithms. This is primarily fundamental science, but the results will be tested with industrial collaborators on real-world combinatorial optimisation problems—the kind that underpin logistics, scheduling, network design, and supply chain management. A deeper theoretical understanding could eventually lead to faster, more predictable algorithms for systems that quietly keep modern infrastructure running.
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Bio-Inspired Search Heuristics (BISHs) are general purpose randomized search heuristics (RSHs). Well known BISHs are Evolutionary Algorithms, Ant Colony Optimisation and Artificial Immune Systems. They have been applied successfully to combinatorial optimization in many fields. However, their computational complexity is far from being understood in depth. In this project the mathematical methodology will be developed to reveal where the real power of BISHs is in comparison with the traditional problem-specific algorithms. The project impacts the field of BISHs in several ways. A feature that distinguishes BISHs from most other algorithms is their population of individuals that simultaneously explore the search space. The first objective is to explain the performance of realistic BISHs for well-known combinatorial optimization problems through runtime analyses, highlighting the relationships between the solution quality and the exploration capabilities of the population. The second objective is to theoretically explain how BISHs can take advantage of the parallelisation available inherently in new technologies to achieve the population diversity required to produce solutions of higher quality in shorter time. The third objective of this project is to create a mathematical basis to explain the working principles of Genetic Programming (GP) and allow the effective and efficient self-evolution of computer programs. The fourth objective is to devise a suitable computational complexity model for the problem classification of BISHs. The enlargement of the established computational complexity picture with BISH complexity classes will enable the understanding of the relationships between traditional problem-specific algorithms and BISHs. Through industrial collaborators, the final objective is the direct exploitation of the theoretical results in real-world applications related to the combinatorial optimization problems studied in this project.
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