arXiv subjects

Frank Neumann

Publications and source records attributed to Frank Neumann.

At least 73 records · Page 4Linked to original sources

arXiv2023

Evolutionary Diversity Optimisation in Constructing Satisfying Assignments

Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the context of EDO. SAT is of great importance in computer science and differs from the other problems studied in EDO literature, such as KP and TSP. SAT is heavily constrained, and the conventional evolutionary operators are inefficient in generating SAT solutions. Our approach avails of the following characteristics of SAT: 1) the possibility of adding more constraints (clauses) to the problem to forbid solutions or to fix variables, and 2) powerful solvers in the literature, such as minisat. We utilise such a solver to construct a diverse set of solutions. Moreover, maximising diversity provides us with invaluable information about the solution space of a given SAT problem, such as how large the feasible region is. In this study, we introduce evolutionary algorithms (EAs) employing a well-known SAT solver to maximise diversity among a set of SAT solutions explicitly. The experimental investigations indicate the introduced algorithms' capability to maximise diversity among the SAT solutions.

cs.NE↗

arXiv2023

Fast Pareto Optimization Using Sliding Window Selection

Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good approximations is the population size of the algorithms which grows with the number of trade-offs that the algorithms encounter. In this paper, we introduce a sliding window speed up technique for recently introduced algorithms. We prove that our technique eliminates the population size as a crucial factor negatively impacting the runtime and achieves the same theoretical performance guarantees as previous approaches within less computation time. Our experimental investigations for the classical maximum coverage problem confirms that our sliding window technique clearly leads to better results for a wide range of instances and constraint settings.

cs.NE↗

arXiv2023

Towards Self-adaptive Mutation in Evolutionary Multi-Objective Algorithms

Parameter control has succeeded in accelerating the convergence process of evolutionary algorithms. While empirical and theoretical studies have shed light on the behavior of algorithms for single-objective optimization, little is known about how self-adaptation influences multi-objective evolutionary algorithms. In this work, we contribute (1) extensive experimental analysis of the Global Simple Evolutionary Multi-objective Algorithm (GSEMO) variants on classic problems, such as OneMinMax, LOTZ, COCZ, and (2) a novel version of GSEMO with self-adaptive mutation. To enable self-adaptation in GSEMO, we explore three self-adaptive mutation techniques from single-objective optimization and use various performance metrics, such as hypervolume and inverted generational distance, to guide the adaptation. Our experiments show that adapting the mutation rate based on single-objective optimization and hypervolume can speed up the convergence of GSEMO. Moreover, we propose a GSEMO with self-adaptive mutation, which considers optimizing for single objectives and adjusts the mutation rate for each solution individually. Our results demonstrate that the proposed method outperforms the GSEMO with static mutation rates across all the tested problems. This work provides a comprehensive benchmarking study for MOEAs and complements existing theoretical runtime analysis. Our proposed algorithm addresses interesting issues for designing MOEAs for future practical applications.

cs.NE↗

arXiv2023

3-Objective Pareto Optimization for Problems with Chance Constraints

Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem.

cs.NE↗

arXiv2023

Evolving Reinforcement Learning Environment to Minimize Learner's Achievable Reward: An Application on Hardening Active Directory Systems

We study a Stackelberg game between one attacker and one defender in a configurable environment. The defender picks a specific environment configuration. The attacker observes the configuration and attacks via Reinforcement Learning (RL trained against the observed environment). The defender's goal is to find the environment with minimum achievable reward for the attacker. We apply Evolutionary Diversity Optimization (EDO) to generate diverse population of environments for training. Environments with clearly high rewards are killed off and replaced by new offsprings to avoid wasting training time. Diversity not only improves training quality but also fits well with our RL scenario: RL agents tend to improve gradually, so a slightly worse environment earlier on may become better later. We demonstrate the effectiveness of our approach by focusing on a specific application, Active Directory (AD). AD is the default security management system for Windows domain networks. AD environment describes an attack graph, where nodes represent computers/accounts/etc., and edges represent accesses. The attacker aims to find the best attack path to reach the highest-privilege node. The defender can change the graph by removing a limited number of edges (revoke accesses). Our approach generates better defensive plans than the existing approach and scales better.

cs.NE↗

arXiv2023

Fixed Parameter Multi-Objective Evolutionary Algorithms for the W-Separator Problem

Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of evolutionary multi-objective algorithms for the $W$-separator problem, which is a natural generalization of the vertex cover problem. The goal is to remove the minimum number of vertices such that each connected component in the resulting graph has at most $W$ vertices. We provide different multi-objective formulations involving two or three objectives that provably lead to fixed-parameter evolutionary algorithms with respect to the value of an optimal solution $OPT$ and $W$. Of particular interest are kernelizations and the reducible structures used for them. We show that in expectation the algorithms make incremental progress in finding such structures and beyond. The current best known kernelization of the $W$-separator uses linear programming methods and requires a non-trivial post-process to extract the reducible structures. We provide additional structural features to show that evolutionary algorithms with appropriate objectives are also capable of extracting them. Our results show that evolutionary algorithms with different objectives guide the search and admit fixed parameterized runtimes to solve or approximate (even arbitrarily close) the $W$-separator problem.

math.CO↗

arXiv2023

Evolutionary Multi-Objective Algorithms for the Knapsack Problems with Stochastic Profits

Evolutionary multi-objective algorithms have been widely shown to be successful when utilized for a variety of stochastic combinatorial optimization problems. Chance constrained optimization plays an important role in complex real-world scenarios, as it allows decision makers to take into account the uncertainty of the environment. We consider a version of the knapsack problem with stochastic profits to guarantee a certain level of confidence in the profit of the solutions. We introduce the multi-objective formulations of the profit chance constrained knapsack problem and design three bi-objective fitness evaluation methods that work independently of the specific confidence level required. We evaluate our approaches using well-known multi-objective evolutionary algorithms GSEMO and NSGA-II. In addition, we introduce a filtering method for GSEMO that improves the quality of the final population by periodically removing certain solutions from the interim populations based on their confidence level. We show the effectiveness of our approaches on several benchmarks for both settings where the knapsack items have fixed uniform uncertainties and uncertainties that are positively correlated with the expected profit of an item.

cs.NE↗

arXiv2023

Benchmarking Algorithms for Submodular Optimization Problems Using IOHProfiler

Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for a wide class of submodular problems under various types of constraints while clearly outperforming standard greedy approximation algorithms. This paper introduces a setup for benchmarking algorithms for submodular optimization problems with the aim to provide researchers with a framework to enhance and compare the performance of new algorithms for submodular problems. The focus is on the development of iterative search algorithms such as evolutionary algorithms with the implementation provided and integrated into IOHprofiler which allows for tracking and comparing the progress and performance of iterative search algorithms. We present a range of submodular optimization problems that have been integrated into IOHprofiler and show how the setup can be used for analyzing and comparing iterative search algorithms in various settings.

cs.AI↗

arXiv2023

On the Use of Quality Diversity Algorithms for The Traveling Thief Problem

In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The traveling thief problem~(TTP) belongs to this category and is formed by the integration of the traveling salesperson problem~(TSP) and the knapsack problem~(KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity~(QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quality solutions but also to illustrate the distribution of high-performing solutions in the behavioural space. We introduce a MAP-Elite based evolutionary algorithm using well-known TSP and KP search operators, taking the TSP and KP score as the behavioural descriptor. Afterwards, we conduct comprehensive experimental studies that show the usefulness of using the QD approach applied to the TTP. First, we provide insights regarding high-quality TTP solutions in the TSP/KP behavioural space. Afterwards, we show that better solutions for the TTP can be obtained by using our QD approach and it can improve the best-known solution for a number of TTP instances used for benchmarking in the literature.

cs.NE↗

arXiv2023

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.

cs.NE↗

arXiv2022

Scalable Edge Blocking Algorithms for Defending Active Directory Style Attack Graphs

Active Directory (AD) is the default security management system for Windows domain networks. An AD environment naturally describes an attack graph where nodes represent computers/accounts/security groups, and edges represent existing accesses/known exploits that allow the attacker to gain access from one node to another. Motivated by practical AD use cases, we study a Stackelberg game between one attacker and one defender. There are multiple entry nodes for the attacker to choose from and there is a single target (Domain Admin). Every edge has a failure rate. The attacker chooses the attack path with the maximum success rate. The defender can block a limited number of edges (i.e., revoke accesses) from a set of blockable edges, limited by budget. The defender's aim is to minimize the attacker's success rate. We exploit the tree-likeness of practical AD graphs to design scalable algorithms. We propose two novel methods that combine theoretical fixed parameter analysis and practical optimisation techniques. For graphs with small tree widths, we propose a tree decomposition based dynamic program. We then propose a general method for converting tree decomposition based dynamic programs to reinforcement learning environments, which leads to an anytime algorithm that scales better, but loses the optimality guarantee. For graphs with small numbers of non-splitting paths (a parameter we invent specifically for AD graphs), we propose a kernelization technique that significantly downsizes the model, which is then solved via mixed-integer programming. Experimentally, our algorithms scale to handle synthetic AD graphs with tens of thousands of nodes.

cs.CR↗

arXiv2022

Theoretical Study of Optimizing Rugged Landscapes with the cGA

Estimation of distribution algorithms (EDAs) provide a distribution - based approach for optimization which adapts its probability distribution during the run of the algorithm. We contribute to the theoretical understanding of EDAs and point out that their distribution approach makes them more suitable to deal with rugged fitness landscapes than classical local search algorithms. Concretely, we make the OneMax function rugged by adding noise to each fitness value. The cGA can nevertheless find solutions with n(1 - ε) many 1s, even for high variance of noise. In contrast to this, RLS and the (1+1) EA, with high probability, only find solutions with n(1/2+o(1)) many 1s, even for noise with small variance.

cs.NE↗

arXiv2022

Analysis of Evolutionary Diversity Optimisation for Permutation Problems

Generating diverse populations of high quality solutions has gained interest as a promising extension to the traditional optimization tasks. This work contributes to this line of research with an investigation on evolutionary diversity optimization for three of the most well-studied permutation problems, namely the Traveling Salesperson Problem (TSP), both symmetric and asymmetric variants, and Quadratic Assignment Problem (QAP). It includes an analysis of the worst-case performance of a simple mutation-only evolutionary algorithm with different mutation operators, using an established diversity measure. Theoretical results show many mutation operators for these problems guarantee convergence to maximally diverse populations of sufficiently small size within cubic to quartic expected run-time. On the other hand, the result on QAP suggests that strong mutations give poor worst-case performance, as mutation strength contributes exponentially to the expected run-time. Additionally, experiments are carried out on QAPLIB and synthetic instances in unconstrained and constrained settings, and reveal much more optimistic practical performances, while corroborating the theoretical finding regarding mutation strength. These results should serve as a baseline for future studies.

cs.NE↗

arXiv2022

Runtime Analysis of the (1+1) EA on Weighted Sums of Transformed Linear Functions

Linear functions play a key role in the runtime analysis of evolutionary algorithms and studies have provided a wide range of new insights and techniques for analyzing evolutionary computation methods. Motivated by studies on separable functions and the optimization behaviour of evolutionary algorithms as well as objective functions from the area of chance constrained optimization, we study the class of objective functions that are weighted sums of two transformed linear functions. Our results show that the (1+1) EA, with a mutation rate depending on the number of overlapping bits of the functions, obtains an optimal solution for these functions in expected time O(n log n), thereby generalizing a well-known result for linear functions to a much wider range of problems.

cs.NE↗

arXiv2022

Co-Evolutionary Diversity Optimisation for the Traveling Thief Problem

Recently different evolutionary computation approaches have been developed that generate sets of high quality diverse solutions for a given optimisation problem. Many studies have considered diversity 1) as a mean to explore niches in behavioural space (quality diversity) or 2) to increase the structural differences of solutions (evolutionary diversity optimisation). In this study, we introduce a co-evolutionary algorithm to simultaneously explore the two spaces for the multi-component traveling thief problem. The results show the capability of the co-evolutionary algorithm to achieve significantly higher diversity compared to the baseline evolutionary diversity algorithms from the the literature.

cs.NE↗

arXiv2022

Analysis of Quality Diversity Algorithms for the Knapsack Problem

Quality diversity (QD) algorithms have been shown to be very successful when dealing with problems in areas such as robotics, games and combinatorial optimization. They aim to maximize the quality of solutions for different regions of the so-called behavioural space of the underlying problem. In this paper, we apply the QD paradigm to simulate dynamic programming behaviours on knapsack problem, and provide a first runtime analysis of QD algorithms. We show that they are able to compute an optimal solution within expected pseudo-polynomial time, and reveal parameter settings that lead to a fully polynomial randomised approximation scheme (FPRAS). Our experimental investigations evaluate the different approaches on classical benchmark sets in terms of solutions constructed in the behavioural space as well as the runtime needed to obtain an optimal solution.

cs.NE↗

arXiv2022

Computing High-Quality Solutions for the Patient Admission Scheduling Problem using Evolutionary Diversity Optimisation

Diversification in a set of solutions has become a hot research topic in the evolutionary computation community. It has been proven beneficial for optimisation problems in several ways, such as computing a diverse set of high-quality solutions and obtaining robustness against imperfect modeling. For the first time in the literature, we adapt the evolutionary diversity optimisation for a real-world combinatorial problem, namely patient admission scheduling. We introduce an evolutionary algorithm to achieve structural diversity in a set of solutions subjected to the quality of each solution. We also introduce a mutation operator biased towards diversity maximisation. Finally, we demonstrate the importance of diversity for the aforementioned problem through a simulation.

cs.NE↗

arXiv2022

Evolutionary Time-Use Optimization for Improving Children's Health Outcomes

How someone allocates their time is important to their health and well-being. In this paper, we show how evolutionary algorithms can be used to promote health and well-being by optimizing time usage. Based on data from a large population-based child cohort, we design fitness functions to explain health outcomes and introduce constraints for viable time plans. We then investigate the performance of evolutionary algorithms to optimize time use for four individual health outcomes with hypothetical children with different day structures. As the four health outcomes are competing for time allocations, we study how to optimize multiple health outcomes simultaneously in the form of a multi-objective optimization problem. We optimize one-week time-use plans using evolutionary multi-objective algorithms and point out the trade-offs achievable with respect to different health outcomes.

cs.NE↗