The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is one of the most prominent algorithms to solve multi-objective optimization problems. Recently, the first mathematical runtime guarantees have been obtained for this algorithm, however only for synthetic benchmark problems. In this work, we give the first proven performance guarantees for a classic optimization problem, the NP-complete bi-objective minimum spanning tree problem. More specifically, we show that the NSGA-II with population size $N \ge 4((n-1) w_{\max} + 1)$ computes all extremal points of the Pareto front in an expected number of $O(m^2 n w_{\max} \log(n w_{\max}))$ iterations, where $n$ is the number of vertices, $m$ the number of edges, and $w_{\max}$ is the maximum edge weight in the problem instance. This result confirms, via mathematical means, the good performance of the NSGA-II observed empirically. It also shows that mathematical analyses of this algorithm are not only possible for synthetic benchmark problems, but also for more complex combinatorial optimization problems. As a side result, we also obtain a new analysis of the performance of the global SEMO algorithm on the bi-objective minimum spanning tree problem, which improves the previous best result by a factor of $|F|$, the number of extremal points of the Pareto front, a set that can be as large as $n w_{\max}$. The main reason for this improvement is our observation that both multi-objective evolutionary algorithms find the different extremal points in parallel rather than sequentially, as assumed in the previous proofs.

Applications, such as military and disaster response, can benefit from robotic collectives' ability to perform multiple cooperative tasks (e.g., surveillance, damage assessments) efficiently across a large spatial area. Coalition formation algorithms can potentially facilitate collective robots' assignment to appropriate task teams; however, most coalition formation algorithms were designed for smaller multiple robot systems (i.e., 2-50 robots). Collectives' scale and domain-relevant constraints (i.e., distribution, near real-time, minimal communication) make coalition formation more challenging. This manuscript identifies the challenges inherent to designing coalition formation algorithms for very large collectives (e.g., 1000 robots). A survey of multiple robot coalition formation algorithms finds that most are unable to transfer directly to collectives, due to the identified system differences; however, auctions and hedonic games may be the most transferable. A simulation-based evaluation of three auction and hedonic game algorithms, applied to homogeneous and heterogeneous collectives, demonstrates that there are collective compositions for which no existing algorithm is viable; however, the experimental results and literature survey suggest paths forward.

Trajectory optimization of a robot manipulator consists of both optimization of the robot movement as well as optimization of the robot end-effector path. This paper aims to find optimum movement parameters including movement type, speed, and acceleration to minimize robot energy. Trajectory optimization by minimizing the energy would increase the longevity of robotic manipulators. We utilized the particle swarm optimization method to find the movement parameters leading to minimum energy consumption. The effectiveness of the proposed method is demonstrated on different trajectories. Experimental results show that 49% efficiency was obtained using a UR5 robotic arm.

We survey eight recent works by our group, involving the successful blending of evolutionary algorithms with machine learning and deep learning: 1. Binary and Multinomial Classification through Evolutionary Symbolic Regression, 2. Classy Ensemble: A Novel Ensemble Algorithm for Classification, 3. EC-KitY: Evolutionary Computation Tool Kit in Python, 4. Evolution of Activation Functions for Deep Learning-Based Image Classification, 5. Adaptive Combination of a Genetic Algorithm and Novelty Search for Deep Neuroevolution, 6.

This paper presents an extended version of Deeper, a search-based simulation-integrated test solution that generates failure-revealing test scenarios for testing a deep neural network-based lane-keeping system. In the newly proposed version, we utilize a new set of bio-inspired search algorithms, genetic algorithm (GA), $({\mu}+{\lambda})$ and $({\mu},{\lambda})$ evolution strategies (ES), and particle swarm optimization (PSO), that leverage a quality population seed and domain-specific cross-over and mutation operations tailored for the presentation model used for modeling the test scenarios. In order to demonstrate the capabilities of the new test generators within Deeper, we carry out an empirical evaluation and comparison with regard to the results of five participating tools in the cyber-physical systems testing competition at SBST 2021. Our evaluation shows the newly proposed test generators in Deeper not only represent a considerable improvement on the previous version but also prove to be effective and efficient in provoking a considerable number of diverse failure-revealing test scenarios for testing an ML-driven lane-keeping system. They can trigger several failures while promoting test scenario diversity, under a limited test time budget, high target failure severity, and strict speed limit constraints.

The ongoing deep learning revolution has allowed computers to outclass humans in various games and perceive features imperceptible to humans during classification tasks. Current machine learning techniques have clearly distinguished themselves in specialized tasks. However, we have yet to see robots capable of performing multiple tasks at an expert level. Most work in this field is focused on the development of more sophisticated learning algorithms for a robot's controller given a largely static and presupposed robotic design. By focusing on the development of robotic bodies, rather than neural controllers, I have discovered that robots can be designed such that they overcome many of the current pitfalls encountered by neural controllers in multitask settings. Through this discovery, I also present novel metrics to explicitly measure the learning ability of a robotic design and its resistance to common problems such as catastrophic interference. Traditionally, the physical robot design requires human engineers to plan every aspect of the system, which is expensive and often relies on human intuition. In contrast, within the field of evolutionary robotics, evolutionary algorithms are used to automatically create optimized designs, however, such designs are often still limited in their ability to perform in a multitask setting. The metrics created and presented here give a novel path to automated design that allow evolved robots to synergize with their controller to improve the computational efficiency of their learning while overcoming catastrophic interference. Overall, this dissertation intimates the ability to automatically design robots that are more general purpose than current robots and that can perform various tasks while requiring less computation.

We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time in the oracle model, the parameter being the number of objectives. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.

Balanced circular bin packing problems consist in positioning a given number of weighted circles in order to minimize the radius of a circular container while satisfying equilibrium constraints. These problems are NP-hard, highly constrained and dimensional. This paper describes a swarm algorithm based on a virtual-force system in order to solve balanced circular bin packing problems. In the proposed approach, a system of forces is applied to each component allowing to take into account the constraints and minimizing the objective function using the fundamental principle of dynamics. The proposed algorithm is experimented and validated on benchmarks of various balanced circular bin packing problems with up to 300 circles. The reported results allow to assess the effectiveness of the proposed approach compared to existing results from the literature.

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (1) TO and (2) ML perspectives. The TO perspective addresses "why" to use ML for TO, while the ML perspective addresses "how" to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined.

We study the problem of efficiently generating differentially private synthetic data that approximate the statistical properties of an underlying sensitive dataset. In recent years, there has been a growing line of work that approaches this problem using first-order optimization techniques. However, such techniques are restricted to optimizing differentiable objectives only, severely limiting the types of analyses that can be conducted. For example, first-order mechanisms have been primarily successful in approximating statistical queries only in the form of marginals for discrete data domains. In some cases, one can circumvent such issues by relaxing the task's objective to maintain differentiability. However, even when possible, these approaches impose a fundamental limitation in which modifications to the minimization problem become additional sources of error. Therefore, we propose Private-GSD, a private genetic algorithm based on zeroth-order optimization heuristics that do not require modifying the original objective. As a result, it avoids the aforementioned limitations of first-order optimization. We empirically evaluate Private-GSD against baseline algorithms on data derived from the American Community Survey across a variety of statistics--otherwise known as statistical queries--both for discrete and real-valued attributes. We show that Private-GSD outperforms the state-of-the-art methods on non-differential queries while matching accuracy in approximating differentiable ones.