Artificial Immune Systems for Combinatorial Optimisation: A Theoretical Investigation

We focus on the clonal selection inspired computational models of the immune system developed for general-purpose optimisation. Our aim is to highlight when these artificial immune systems (AIS) are more efficient than evolutionary algorithms (EAs). Compared to traditional EAs, AIS use considerably higher mutation rates (hypermutations) for variation, give higher selection probabilities to more recent solutions and lower selection probabilities to older ones (ageing). We consider the standard Opt-IA that includes both of the AIS distinguishing features and argue why it is of greater applicability than other popular AIS. Our first result is the proof that the stop at first constructive mutation version of its hypermutation operator is essential. Without it, the hypermutations cannot optimise any function with an arbitrary polynomial number of optima. Afterwards we show that the hypermutations are exponentially faster than the standard bit mutation operator used in traditional EAs at escaping from local optima of standard benchmark function classes and of the NP-hard Partition problem. If the basin of attraction of the local optima is not too large, then ageing allows even greater speed-ups. For the Cliff benchmark function this can make the difference between exponential and quasi-linear expected time. If the basin of attraction is too large, then ageing can implicitly detect the local optimum and escape it by automatically restarting the search process. The described power of hypermutations and ageing allows us to prove that they guarantee (1+epsilon) approximations for Partition in expected polynomial time for any constant epsilon. These features come at the expense of the hypermutations being a linear factor slower than EAs for standard unimodal benchmark functions and of eliminating the power of ageing at escaping local optima in the complete Opt-IA. We show that hypermutating with inversely proportional rates mitigates such drawbacks at the expense of losing the explorative advantages of the standard operator. We conclude the thesis by designing fast hypermutation operators that are provably a linear factor faster than the traditional ones for the unimodal benchmark functions and Partition, while maintaining explorative power and working in harmony together with ageing

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades:Part B

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part paper, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms, namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multi-population methods, which are under-represented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an indepth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the dynamic optimization algorithms, and dynamic real-world applications. Finally, several opportunities for future work are pointed out

A survey of evolutionary continuous dynamic optimization over two decades – part A

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part paper, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms, namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multi-population methods, which are under-represented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an indepth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the dynamic optimization algorithms, and dynamic real-world applications. Finally, several opportunities for future work are pointed out

Robust optimization over time : a critical review

Robust optimization over time (ROOT) is the combination of robust optimization and dynamic optimization. In ROOT, frequent changes to deployed solutions are undesirable, which can be due to the high cost of switching between deployed solutions, limitations on the resources required to deploy new solutions, and/or the system’s inability to tolerate frequent changes in the deployed solutions. ROOT is dedicated to the study and development of algorithms capable of dealing with the implications of deploying or maintaining solutions over longer time horizons involving multiple environmental changes. This paper presents an in-depth review of the research on ROOT. The overarching aim of this survey is to help researchers gain a broad perspective on the current state of the field, what has been achieved so far, and the existing challenges and pitfalls. This survey also aims to improve accessibility and clarity by standardizing terminology and unifying mathematical notions used across the field, providing explicit mathematical formulations of definitions, and improving many existing mathematical descriptions. Moreover, we classify ROOT problems based on two ROOT-specific criteria: the requirements for changing or keeping deployed solutions and the number of deployed solutions. This classification helps researchers gain a better understanding of the characteristics and requirements of ROOT problems, which is crucial to systematic algorithm design and benchmarking. Additionally, we classify ROOT methods based on the approach they use for finding robust solutions and provide a comprehensive review of them. This survey also reviews ROOT benchmarks and performance indicators. Finally, we identify several future research directions

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades - Part A

Yazdani D, Cheng R, Yazdani D, Branke J, Jin Y, Yao X. A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades - Part A. IEEE Transactions on Evolutionary Computation. 2021;25(4):609-629.Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part article, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms (DOAs), namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multipopulation methods, which are underrepresented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an in-depth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the DOAs, and dynamic real-world applications. Finally, several opportunities for future work are pointed out

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades - Part B

Yazdani D, Cheng R, Yazdani D, Branke J, Jin Y, Yao X. A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades - Part B. IEEE Transactions on Evolutionary Computation. 2021;25(4):630-650.This article presents the second Part of a two-Part survey that reviews evolutionary dynamic optimization (EDO) for single-objective unconstrained continuous problems over the last two decades. While in the first part, we reviewed the components of dynamic optimization algorithms (DOAs); in this part, we present an in-depth review of the most commonly used benchmark problems, performance analysis methods, static optimization methods used in the framework of DOAs, and real-world applications. Compared to the previous works, this article provides a new taxonomy for the benchmark problems used in the field based on their baseline functions and dynamics. In addition, this survey classifies the commonly used performance indicators into fitness/error-based and efficiency-based ones. Different types of plots used in the literature for analyzing the performance and behavior of algorithms are also reviewed. Furthermore, the static optimization algorithms that are modified and utilized in the framework of DOAs as the optimization components are covered. We then comprehensively review some real-world dynamic problems that are optimized by EDO methods. Finally, some challenges and opportunities are pointed out for future directions