Large language models (LLMs) have revolutionized natural language processing by solving a wide range of tasks simply guided by a prompt. Yet their performance is highly sensitive to prompt formulation. While automated prompt optimization addresses this challenge by finding optimal prompts, current methods require a substantial number of LLM calls and input tokens, making prompt optimization expensive. We introduce CAPO (Cost-Aware Prompt Optimization), an algorithm that enhances prompt optimization efficiency by integrating AutoML techniques. CAPO is an evolutionary approach with LLMs as operators, incorporating racing to save evaluations and multi-objective optimization to balance performance with prompt length. It jointly optimizes instructions and few-shot examples while leveraging task descriptions for improved robustness. Our extensive experiments across diverse datasets and LLMs demonstrate that CAPO outperforms state-of-the-art discrete prompt optimization methods in 11/15 cases with improvements up to 21%p. Our algorithm achieves better performances already with smaller budgets, saves evaluations through racing, and decreases average prompt length via a length penalty, making it both cost-efficient and cost-aware. Even without few-shot examples, CAPO outperforms its competitors and generally remains robust to initial prompts. CAPO represents an important step toward making prompt optimization more powerful and accessible by improving cost-efficiency.

Caroline Panggabean Department of CSE (AI) JAIN (Deemed - to - be University) Bangalore, Karnataka carolinepgabean@gmail.com ORCID: https://orcid.org/0009 - 0004 - 9964 - 7986 Ranju Limbu Department of CSE (AIM) JAIN (Deemed - to - be University) Bangalore, Karnataka 21btlca002 @jainuniversity.ac.in Dr. Devaraj Verma C Department of CSE (AI) JAIN (Deemed - to - be University) Bangalore, Karnataka c.devaraj@jainuniversity.ac.in ORCID: https://orcid.org/0000 - 0002 - 1504 - 4263 Rhythm Sarker Department of CSE (AIML) JAIN (Deemed - to - be University) Bangalore, Karnataka 21btrca065 @jainuniversity.ac.in Bhagyashree Gogoi Department of CSE (AI) JAIN (Deemed - to - be University) Bangalore, Karnataka 21btlca001 @ jainuniver s ity.ac.in Abstract -- Cloud computing environments demand dynamic and efficient resource management to ensure optimal performance, reduced energy consumption, and adherence to Service Level Agreements (SLAs). This paper presents a Genetic Algorithm (GA) - based approach for Virtual Machine (VM) placement and consol idation, aiming to minimize power usage while maintaining QoS constraints. The proposed method dynamically adjusts VM allocation based on real - time workload variations, outperforming traditional heuristics such as First Fit Decreasing (FFD) and Best Fit De creasing (BFD). Experimental results show notable reductions in energy consumption, VM migrations, SLA violation rates, and execution time.

--Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints, and each represents a well-developed field. Despite addressing similar problems, their connection remains largely unexplored. By demonstrating this equivalence, we provide a unified perspective on these techniques. This unification has theoretical and practical implications, facilitating the cross-application of robustness guarantees and algorithmic improvements between complementarity and CBF frameworks. We discuss these synergistic benefits and motivate future work in the comparison of the methods in more general cases.

Recent research in Cooperative Coevolution~(CC) have achieved promising progress in solving large-scale global optimization problems. However, existing CC paradigms have a primary limitation in that they require deep expertise for selecting or designing effective variable decomposition strategies. Inspired by advancements in Meta-Black-Box Optimization, this paper introduces LCC, a pioneering learning-based cooperative coevolution framework that dynamically schedules decomposition strategies during optimization processes. The decomposition strategy selector is parameterized through a neural network, which processes a meticulously crafted set of optimization status features to determine the optimal strategy for each optimization step. The network is trained via the Proximal Policy Optimization method in a reinforcement learning manner across a collection of representative problems, aiming to maximize the expected optimization performance. Extensive experimental results demonstrate that LCC not only offers certain advantages over state-of-the-art baselines in terms of optimization effectiveness and resource consumption, but it also exhibits promising transferability towards unseen problems.

The rapid electrification of transportation, driven by stringent decarbonization targets and supportive policies, poses significant challenges for distribution system operators (DSOs). When numerous electric vehicles (EVs) charge concurrently, local transformers risk overloading - a problem that current tariff-based strategies do not adequately address. This paper introduces an aggregator-based coordination mechanism that shifts EV charging from congested to underutilized periods using a rule-based scheduling algorithm. Unlike conventional methods that depend on complex real-time pricing signals or optimization-heavy solutions, the aggregator approach uses a simple yet effective "laxity" measure to prioritize charging flexibility. To assess technical and economic viability, a multi-agent simulation was developed to replicate residential user behavior and DSO constraints under the use of a 400 kVA low-voltage transformer. The results indicate that overloads are completely eliminated with minimal inconvenience to users, whose increased charging costs are offset by the aggregator at an annual total of under DKK 6000 - significantly lower than the cost of infrastructure reinforcement. This study contributes by (i) quantifying the compensation needed to prevent large-scale overloads, (ii) presenting a replicable, computationally feasible, rule-based aggregator model for DSOs, and (iii) comparing aggregator solutions to costly transformer upgrades, underscoring the aggregator's role as a viable tool for future distribution systems.

Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems due to the curse of dimensionality. This dissertation explores the path integral control framework as a scalable, sampling-based alternative. By reformulating SOC problems as expectations over stochastic trajectories, it enables efficient policy synthesis via Monte Carlo sampling and supports real-time implementation through GPU parallelization. We apply this framework to six classes of SOC problems: Chance-Constrained SOC, Stochastic Differential Games, Deceptive Control, Task Hierarchical Control, Risk Mitigation of Stealthy Attacks, and Discrete-Time LQR. A sample complexity analysis for the discrete-time case is also provided. These contributions establish a foundation for simulator-driven autonomy in complex, uncertain environments.

The challenge of noisy multi-objective optimization lies in the constant trade-off between exploring new decision points and improving the precision of known points through resampling. This decision should take into account both the variability of the objective functions and the current estimate of a point in relation to the Pareto front. Since the amount and distribution of noise are generally unknown, it is desirable for a decision function to be highly adaptive to the properties of the optimization problem. This paper presents a resampling decision function that incorporates the stochastic nature of the optimization problem by using bootstrapping and the probability of dominance. The distribution-free estimation of the probability of dominance is achieved using bootstrap estimates of the means. To make the procedure applicable even with very few observations, we transfer the distribution observed at other decision points. The efficiency of this resampling approach is demonstrated by applying it in the NSGA-II algorithm with a sequential resampling procedure under multiple noise variations.

In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting them in which the edges are traversed in increasing order of their labels. We study the problem of scheduling the availability time of the edges of a temporal graph in such a way that all pairs of vertices are connected within a given maximum allowed time $a$ and the overall number of labels is minimized. The problem, known as \emph{Minimum Aged Labeling} (MAL), has several applications in logistics, distribution scheduling, and information spreading in social networks, where carefully choosing the time-labels can significantly reduce infrastructure costs, fuel consumption, or greenhouse gases. The problem MAL has previously been proved to be NP-complete on undirected graphs and \APX-hard on directed graphs. In this paper, we extend our knowledge on the complexity and approximability of MAL in several directions. We first show that the problem cannot be approximated within a factor better than $O(\log n)$ when $a\geq 2$, unless $\text{P} = \text{NP}$, and a factor better than $2^{\log ^{1-ε} n}$ when $a\geq 3$, unless $\text{NP}\subseteq \text{DTIME}(2^{\text{polylog}(n)})$, where $n$ is the number of vertices in the graph. Then we give a set of approximation algorithms that, under some conditions, almost match these lower bounds. In particular, we show that the approximation depends on a relation between $a$ and the diameter of the input graph. We further establish a connection with a foundational optimization problem on static graphs called \emph{Diameter Constrained Spanning Subgraph} (DCSS) and show that our hardness results also apply to DCSS.

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is correlated with the quality of the solution, the number of parameters to optimize grows linearly. This results in more iterations required by the classical optimizer, which results in an increasing computational burden as more circuit executions are needed. To mitigate this issue, we introduce QAOA-PCA, a novel reparameterization technique that employs Principal Component Analysis (PCA) to reduce the dimensionality of the QAOA parameter space. By extracting principal components from optimized parameters of smaller problem instances, QAOA-PCA facilitates efficient optimization with fewer parameters on larger instances. Our empirical evaluation on the prominent MaxCut problem demonstrates that QAOA-PCA consistently requires fewer iterations than standard QAOA, achieving substantial efficiency gains. While this comes at the cost of a slight reduction in approximation ratio compared to QAOA with the same number of layers, QAOA-PCA almost always outperforms standard QAOA when matched by parameter count. QAOA-PCA strikes a favorable balance between efficiency and performance, reducing optimization overhead without significantly compromising solution quality.

Traditional Partial Least Squares Regression (PLSR) models frequently underperform when handling data characterized by uneven categories. To address the issue, this paper proposes a Data Augmentation Partial Least Squares Regression (DAPLSR) model via manifold optimization. The DAPLSR model introduces the Synthetic Minority Over-sampling Technique (SMOTE) to increase the number of samples and utilizes the Value Difference Metric (VDM) to select the nearest neighbor samples that closely resemble the original samples for generating synthetic samples. In solving the model, in order to obtain a more accurate numerical solution for PLSR, this paper proposes a manifold optimization method that uses the geometric properties of the constraint space to improve model degradation and optimization. Comprehensive experiments show that the proposed DAPLSR model achieves superior classification performance and outstanding evaluation metrics on various datasets, significantly outperforming existing methods.