Multi-modal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multi-modal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper introduces a multi-modal optimization version of the Big Bang-Big Crunch algorithm based on clustering, namely, k-BBBC. This algorithm guarantees a complete convergence of the entire population, retrieving on average the 99\% of local optima for a specific problem. Additionally, we introduce two post-processing methods to (i) identify the local optima in a set of retrieved solutions (i.e., a population), and (ii) quantify the number of correctly retrieved optima against the expected ones (i.e., success rate). Our results show that k-BBBC performs well even with problems having a large number of optima (tested on 379 optima) and high dimensionality (tested on 32 decision variables). When compared to other multi-modal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) -- especially when elitism is applied. Lastly, we validated our proposed post-processing methods by comparing their success rate to the actual one. Results suggest that these methods can be used to evaluate the performance of a multi-modal optimization algorithm by correctly identifying optima and providing an indication of success -- without the need to know where the optima are located in the search space.

Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small.

Future spacecraft and surface robotic missions require increasingly capable autonomy stacks for exploring challenging and unstructured domains and trajectory optimization will be a cornerstone of such autonomy stacks. However, the nonlinear optimization solvers required remain too slow for use on relatively resource constrained flight-grade computers. In this work, we turn towards amortized optimization, a learning-based technique for accelerating optimization run times, and present TOAST: Trajectory Optimization with Merit Function Warm Starts. Offline, using data collected from a simulation, we train a neural network to learn a mapping to the full primal and dual solutions given the problem parameters. Crucially, we build upon recent results from decision-focused learning and present a set of decision-focused loss functions using the notion of merit functions for optimization problems. We show that training networks with such constraint-informed losses can better encode the structure of the trajectory optimization problem and jointly learn to reconstruct the primal-dual solution while also yielding improved constraint satisfaction. Through numerical experiments on a Lunar rover problem, we demonstrate that TOAST outperforms benchmark approaches in terms of both computation times and network prediction constraint satisfaction.

Deep neural network security is a persistent concern, with considerable research on visible light physical attacks but limited exploration in the infrared domain. Existing approaches, like white-box infrared attacks using bulb boards and QR suits, lack realism and stealthiness. Meanwhile, black-box methods with cold and hot patches often struggle to ensure robustness. To bridge these gaps, we propose Adversarial Infrared Curves (AdvIC). Using Particle Swarm Optimization, we optimize two Bezier curves and employ cold patches in the physical realm to introduce perturbations, creating infrared curve patterns for physical sample generation. Our extensive experiments confirm AdvIC's effectiveness, achieving 94.8\% and 67.2\% attack success rates for digital and physical attacks, respectively. Stealthiness is demonstrated through a comparative analysis, and robustness assessments reveal AdvIC's superiority over baseline methods. When deployed against diverse advanced detectors, AdvIC achieves an average attack success rate of 76.8\%, emphasizing its robust nature. we explore adversarial defense strategies against AdvIC and examine its impact under various defense mechanisms. Given AdvIC's substantial security implications for real-world vision-based applications, urgent attention and mitigation efforts are warranted.

The performance improvement of deep networks significantly depends on their optimizers. With existing optimizers, precise and efficient recognition of the gradients trend remains a challenge. Existing optimizers predominantly adopt techniques based on the first-order exponential moving average (EMA), which results in noticeable delays that impede the real-time tracking of gradients trend and consequently yield sub-optimal performance. To overcome this limitation, we introduce a novel optimizer called fast-adaptive moment estimation (FAME). Inspired by the triple exponential moving average (TEMA) used in the financial domain, FAME leverages the potency of higher-order TEMA to improve the precision of identifying gradient trends. TEMA plays a central role in the learning process as it actively influences optimization dynamics; this role differs from its conventional passive role as a technical indicator in financial contexts. Because of the introduction of TEMA into the optimization process, FAME can identify gradient trends with higher accuracy and fewer lag issues, thereby offering smoother and more consistent responses to gradient fluctuations compared to conventional first-order EMA. To study the effectiveness of our novel FAME optimizer, we conducted comprehensive experiments encompassing six diverse computer-vision benchmarks and tasks, spanning detection, classification, and semantic comprehension. We integrated FAME into 15 learning architectures and compared its performance with those of six popular optimizers. Results clearly showed that FAME is more robust and accurate and provides superior performance stability by minimizing noise (i.e., trend fluctuations). Notably, FAME achieves higher accuracy levels in remarkably fewer training epochs than its counterparts, clearly indicating its significance for optimizing deep networks in computer-vision tasks.

In this work, a novel Stackelberg game theoretic framework is proposed for trading energy bidirectionally between the demand-response (DR) aggregator and the prosumers. This formulation allows for flexible energy arbitrage and additional monetary rewards while ensuring that the prosumers' desired daily energy demand is met. Then, a scalable (linear with the number of prosumers), decentralized, privacy-preserving algorithm is proposed to find approximate equilibria with online sampling and learning of the prosumers' cumulative best response, which finds applications beyond this energy game. Moreover, cost bounds are provided on the quality of the approximate equilibrium solution. Finally, real data from the California day-ahead market and the UC Davis campus building energy demands are utilized to demonstrate the efficacy of the proposed framework and algorithm.

Learning predictive models from observations using deep neural networks (DNNs) is a promising new approach to many real-world planning and control problems. However, common DNNs are too unstructured for effective planning, and current control methods typically rely on extensive sampling or local gradient descent. In this paper, we propose a new framework for integrated model learning and predictive control that is amenable to efficient optimization algorithms. Specifically, we start with a ReLU neural model of the system dynamics and, with minimal losses in prediction accuracy, we gradually sparsify it by removing redundant neurons. This discrete sparsification process is approximated as a continuous problem, enabling an end-to-end optimization of both the model architecture and the weight parameters. The sparsified model is subsequently used by a mixed-integer predictive controller, which represents the neuron activations as binary variables and employs efficient branch-and-bound algorithms. Our framework is applicable to a wide variety of DNNs, from simple multilayer perceptrons to complex graph neural dynamics. It can efficiently handle tasks involving complicated contact dynamics, such as object pushing, compositional object sorting, and manipulation of deformable objects. Numerical and hardware experiments show that, despite the aggressive sparsification, our framework can deliver better closed-loop performance than existing state-of-the-art methods.

Various methods have been proposed to secure access to sensitive information over time, such as the many cryptographic methods in use to facilitate secure communications on the internet. But other methods like steganography have been overlooked which may be more suitable in cases where the act of transmission of sensitive information itself should remain a secret. Multiple techniques that are commonly discussed for such scenarios suffer from low capacity and high distortion in the output signal. This research introduces a novel steganographic approach for concealing a confidential portable document format (PDF) document within a host image by employing the Hybrid Firefly algorithm (HFA) proposed to select the pixel arrangement. This algorithm combines two widely used optimization algorithms to improve their performance. The suggested methodology utilizes the HFA algorithm to conduct a search for optimal pixel placements in the spatial domain. The purpose of this search is to accomplish two main goals: increasing the host image's capacity and reducing distortion. Moreover, the proposed approach intends to reduce the time required for the embedding procedure. The findings indicate a decrease in image distortion and an accelerated rate of convergence in the search process. The resultant embeddings exhibit robustness against steganalytic assaults, hence rendering the identification of the embedded data a formidable undertaking.

Mixed-integer nonlinear programmings (MINLPs) are powerful formulation tools for task planning. However, it suffers from long solving time especially for large scale problems. In this work, we first formulate the task planning problem for item stowing into a mixed-integer nonlinear programming problem, then solve it using Alternative Direction Method of Multipliers (ADMM). ADMM separates the complete formulation into a nonlinear programming problem and mixed-integer programming problem, then iterate between them to solve the original problem. We show that our ADMM converges better than non-warm-started nonlinear complementary formulation. Our proposed methods are demonstrated on hardware as a high level planner to insert books into the bookshelf.

The generation of cold atom clouds is a complex process which involves the optimization of noisy data in high dimensional parameter spaces. Optimization can be challenging both in and especially outside of the lab due to lack of time, expertise, or access for lengthy manual optimization. In recent years, it was demonstrated that machine learning offers a solution since it can optimize high dimensional problems quickly, without knowledge of the experiment itself. In this paper we present results showing the benchmarking of nine different optimization techniques and implementations, alongside their ability to optimize a Rubidium (Rb) cold atom experiment. The investigations are performed on a 3D $^{87}$Rb molasses with 10 and 18 adjustable parameters, respectively, where the atom number obtained by absorption imaging was chosen as the test problem. We further compare the best performing optimizers under different effective noise conditions by reducing the Signal-to-Noise ratio of the images via adapting the atomic vapor pressure in the 2D+ MOT and the detection laser frequency stability.