15 research outputs found
A survey of diversity-oriented optimization
The concept of diversity plays a crucial role in many optimization approaches: On the one hand, diversity can be formulated as an essential goal, such as in level set approximation or multiobjective optimization where the aim is to find a diverse set of alternative feasible or, respectively, Pareto optimal solutions. On the other hand, diversity maintenance can play an important role in algorithms that ultimately searc
Evolving Diverse Sets of Tours for the Travelling Salesperson Problem
Evolving diverse sets of high quality solutions has gained increasing
interest in the evolutionary computation literature in recent years. With this
paper, we contribute to this area of research by examining evolutionary
diversity optimisation approaches for the classical Traveling Salesperson
Problem (TSP). We study the impact of using different diversity measures for a
given set of tours and the ability of evolutionary algorithms to obtain a
diverse set of high quality solutions when adopting these measures. Our studies
show that a large variety of diverse high quality tours can be achieved by
using our approaches. Furthermore, we compare our approaches in terms of
theoretical properties and the final set of tours obtained by the evolutionary
diversity optimisation algorithm.Comment: 11 pages, 3 tables, 3 figures, to be published in GECCO '2
Discrepancy-based Evolutionary Diversity Optimization
Diversity plays a crucial role in evolutionary computation. While diversity
has been mainly used to prevent the population of an evolutionary algorithm
from premature convergence, the use of evolutionary algorithms to obtain a
diverse set of solutions has gained increasing attention in recent years.
Diversity optimization in terms of features on the underlying problem allows to
obtain a better understanding of possible solutions to the problem at hand and
can be used for algorithm selection when dealing with combinatorial
optimization problems such as the Traveling Salesperson Problem. We explore the
use of the star-discrepancy measure to guide the diversity optimization process
of an evolutionary algorithm.
In our experimental investigations, we consider our discrepancy-based
diversity optimization approaches for evolving diverse sets of images as well
as instances of the Traveling Salesperson problem where a local search is not
able to find near optimal solutions. Our experimental investigations comparing
three diversity optimization approaches show that a discrepancy-based diversity
optimization approach using a tie-breaking rule based on weighted differences
to surrounding feature points provides the best results in terms of the star
discrepancy measure
Defending Active Directory by Combining Neural Network based Dynamic Program and Evolutionary Diversity Optimisation
Active Directory (AD) is the default security management system for Windows
domain networks. We study a Stackelberg game model between one attacker and one
defender on an AD attack graph. The attacker initially has access to a set of
entry nodes. The attacker can expand this set by strategically exploring edges.
Every edge has a detection rate and a failure rate. The attacker aims to
maximize their chance of successfully reaching the destination before getting
detected. The defender's task is to block a constant number of edges to
decrease the attacker's chance of success. We show that the problem is #P-hard
and, therefore, intractable to solve exactly. We convert the attacker's problem
to an exponential sized Dynamic Program that is approximated by a Neural
Network (NN). Once trained, the NN provides an efficient fitness function for
the defender's Evolutionary Diversity Optimisation (EDO). The diversity
emphasis on the defender's solution provides a diverse set of training samples,
which improves the training accuracy of our NN for modelling the attacker. We
go back and forth between NN training and EDO. Experimental results show that
for R500 graph, our proposed EDO based defense is less than 1% away from the
optimal defense
Evolutionary Diversity Optimisation for The Traveling Thief Problem
There has been a growing interest in the evolutionary computation community
to compute a diverse set of high-quality solutions for a given optimisation
problem. This can provide the practitioners with invaluable information about
the solution space and robustness against imperfect modelling and minor
problems' changes. It also enables the decision-makers to involve their
interests and choose between various solutions. In this study, we investigate
for the first time a prominent multi-component optimisation problem, namely the
Traveling Thief Problem (TTP), in the context of evolutionary diversity
optimisation. We introduce a bi-level evolutionary algorithm to maximise the
structural diversity of the set of solutions. Moreover, we examine the
inter-dependency among the components of the problem in terms of structural
diversity and empirically determine the best method to obtain diversity. We
also conduct a comprehensive experimental investigation to examine the
introduced algorithm and compare the results to another recently introduced
framework based on the use of Quality Diversity (QD). Our experimental results
show a significant improvement of the QD approach in terms of structural
diversity for most TTP benchmark instances.Comment: To appear at GECCO 202
On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism
Clearing is a niching method inspired by the principle of assigning the available resources
among a niche to a single individual. The clearing procedure supplies these resources only to
the best individual of each niche: the winner. So far, its analysis has been focused on experimental
approaches that have shown that clearing is a powerful diversity-preserving mechanism.
Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that
a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic
distance function always succeeds in optimising all functions of unitation for small niches
in polynomial time, while a genotypic distance function requires exponential time. Finally, we
prove that with phenotypic and genotypic distances clearing is able to find both optima for
Twomax and several general classes of bimodal functions in polynomial expected time. We
use empirical analysis to highlight some of the characteristics that makes it a useful mechanism
and to support the theoretical results
Rigorous Runtime Analysis of Diversity Optimization with GSEMO on OneMinMax
The evolutionary diversity optimization aims at finding a diverse set of
solutions which satisfy some constraint on their fitness. In the context of
multi-objective optimization this constraint can require solutions to be
Pareto-optimal. In this paper we study how the GSEMO algorithm with additional
diversity-enhancing heuristic optimizes a diversity of its population on a
bi-objective benchmark problem OneMinMax, for which all solutions are
Pareto-optimal.
We provide a rigorous runtime analysis of the last step of the optimization,
when the algorithm starts with a population with a second-best diversity, and
prove that it finds a population with optimal diversity in expected time
, when the problem size is odd. For reaching our goal, we analyse
the random walk of the population, which reflects the frequency of changes in
the population and their outcomes.Comment: The full version of the paper accepted to FOGA 2023 conferenc
Evolutionary diversity optimization using multi-objective indicators
Evolutionary diversity optimization aims to compute a set of solutions that are diverse in the search space or instance feature space, and where all solutions meet a given quality criterion. With this paper, we bridge the areas of evolutionary diversity optimization and evolutionary multi-objective optimization. We show how popular indicators frequently used in the area of multi-objective optimization can be used for evolutionary diversity optimization. Our experimental investigations for evolving diverse sets of TSP instances and images according to various features show that two of the most prominent multi-objective indicators, namely the hypervolume indicator and the inverted generational distance, provide excellent results in terms of visualization and various diversity indicators.Aneta Neumann, Wanru Gao, Markus Wagner, Frank Neuman
An evolutionary algorithm for finding diverse sets of molecules with user-defined properties
Abstract The multidisciplinary field of drug discovery deals with the discovery and synthesis of novel medications. For over half a century, Computer Science has aided chemists in exploring the extremely large chemistry space that comprises the set of all drug-like molecules. But only in recent years have the technological advances in computational power and the development of novel algorithms enabled researchers to start experimenting with in silico screening of promising compounds. While many classes of algorithms have been successfully applied in this field, one of the most prevalent is the class of Evolutionary Algorithms (EA). This nature inspired optimization algorithm, which will be discussed in this thesis, allows for the exploration of large search spaces with the goal of finding good solutions to a given problem. Although the classical EA uses the notion of diversity to find solutions, they do not necessarily have the goal of finding a diverse set of solutions. This thesis discusses the application of the novel Evolutionary Level-Set Algorithm (ELSA) for finding not only a good set of solutions, but also for finding a diverse set of molecules given certain constraints on these molecules. This diverse set can be explored by the chemist to enhance creativity and provide a starting point for further research. For the comparison of molecules and to measure similarity, a proper metric is needed, which the algorithm uses to measure the diversity of the population. The ELSA algorithm, along with five different diversity indicators were implemented as an extension module in METool (Molecular Evolutionary Tool). Also, experiments were conducted to test the performance of ELSA and the various diversity indicators in the context of finding diverse sets of molecules with user-defined constraints. The results of the experiments show that the simple measures, despite being of low computational complexity, perform surprisingly well when used as a quality indicator in the ELSA algorithm