Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many-objective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to different problem instances. We propose a methodology to exploit this characteristic by solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We use three goal-based objective functions and show that on benchmark instances of the multiobjective vehicle routing problem with time windows, the methodology is able to produce good results in short computation time. The methodology allows to combine the effectiveness of state-of-the-art multiobjective algorithms with the efficiency of goal programming to find good compromise solutions in problem scenarios where instances have similar fitness landscapes.

Federated learning (FL) has emerged as a promising paradigm within edge computing (EC) systems, enabling numerous edge devices to collaboratively train artificial intelligence (AI) models while maintaining data privacy. To overcome the communication bottlenecks associated with centralized parameter servers, decentralized federated learning (DFL), which leverages peer-to-peer (P2P) communication, has been extensively explored in the research community. Although researchers design a variety of DFL approach to ensure model convergence, its iterative learning process inevitably incurs considerable cost along with the growth of model complexity and the number of participants. These costs are largely influenced by the dynamic changes of topology in each training round, particularly its sparsity and connectivity conditions. Furthermore, the inherent resources heterogeneity in the edge environments affects energy efficiency of learning process, while data heterogeneity degrades model performance. These factors pose significant challenges to the design of an effective DFL framework for EC systems. To this end, we propose Hat-DFed, a heterogeneity-aware and coset-effective decentralized federated learning (DFL) framework. In Hat-DFed, the topology construction is formulated as a dual optimization problem, which is then proven to be NP-hard, with the goal of maximizing model performance while minimizing cumulative energy consumption in complex edge environments. To solve this problem, we design a two-phase algorithm that dynamically constructs optimal communication topologies while unbiasedly estimating their impact on both model performance and energy cost. Additionally, the algorithm incorporates an importance-aware model aggregation mechanism to mitigate performance degradation caused by data heterogeneity.

Endowing humanoid robots with the ability to perform highly dynamic motions akin to human-level acrobatics has been a long-standing challenge. Successfully performing these maneuvers requires close consideration of the underlying physics in both trajectory optimization for planning and control during execution. This is particularly challenging due to humanoids' high degree-of-freedom count and associated exponentially scaling complexities, which makes planning on the explicit equations of motion intractable. Typical workarounds include linearization methods and model approximations. However, neither are sufficient because they produce degraded performance on the true robotic system. This paper presents a control architecture comprising trajectory optimization and whole-body control, intermediated by a matching model abstraction, that enables the execution of acrobatic maneuvers, including constraint and posture behaviors, conditioned on the unabbreviated equations of motion of the articulated rigid body model. A review of underlying modeling and control methods is given, followed by implementation details including model abstraction, trajectory optimization and whole-body controller. The system's effectiveness is analyzed in simulation.

Citizens' assemblies are an increasingly influential form of deliberative democracy, where randomly selected people discuss policy questions. The legitimacy of these assemblies hinges on their representation of the broader population, but participant dropout often leads to an unbalanced composition. In practice, dropouts are replaced by preselected alternates, but existing methods do not address how to choose these alternates. To address this gap, we introduce an optimization framework for alternate selection. Our algorithmic approach, which leverages learning-theoretic machinery, estimates dropout probabilities using historical data and selects alternates to minimize expected misrepresentation. Our theoretical bounds provide guarantees on sample complexity (with implications for computational efficiency) and on loss due to dropout probability mis-estimation. Empirical evaluation using real-world data demonstrates that, compared to the status quo, our method significantly improves representation while requiring fewer alternates.

The hardness of the Unconstrained Binary Quadratic Program (UBQP) problem is due its rugged landscape. Various algorithms have been proposed for UBQP, including the Landscape Smoothing Iterated Local Search (LSILS). Different from other UBQP algorithms, LSILS tries to smooth the rugged landscape by building a convex combination of the original UBQP and a toy UBQP. In this paper, our study further investigates the impact of smoothing rugged landscapes using different toy UBQP problems, including a toy UBQP with matrix ^Q1 (construct by "+/-1"), a toy UBQP with matrix ^Q2 (construct by "+/-i") and a toy UBQP with matrix ^Q3 (construct randomly). We first assess the landscape flatness of the three toy UBQPs. Subsequently, we test the efficiency of LSILS with different toy UBQPs. Results reveal that the toy UBQP with ^Q1 (construct by "+/-1") exhibits the flattest landscape among the three, while the toy UBQP with ^Q3 (construct randomly) presents the most non-flat landscape. Notably, LSILS using the toy UBQP with ^Q2 (construct by "+/-i") emerges as the most effective, while ^Q3 (construct randomly) has the poorest result. These findings contribute to a detailed understanding of landscape smoothing techniques in optimizing UBQP.

Combinatorial optimization problem (COP) is di ffi cult to solve because of the massive number of local optimal solutions in his solution space. V arious methods have been put forward to smooth the solution space of COPs, including homotopic convex (HC) transformation for the traveling salesman problem (TSP). This paper extends the HC transformation approach to unconstrained binary quadratic programming (UBQP) by proposing a method to construct a unimodal toy UBQP of any size. We theoretically prove the unimodality of the constructed toy UBQP . After that, we apply this unimodal toy UBQP to smooth the original UBQP by using the HC transformation framework and empirically verify the smoothing e ff ects. Subsequently, we introduce an iterative algorithmic framework incorporating HC transformation, referred as landscape smoothing iterated local search (LSILS). Our experimental analyses, conducted on various UBQP instances show the e ffectiveness of LSILS. Furthermore, this paper proposes a parallel cooperative variant of LSILS, denoted as PC-LSILS and apply it to both the UBQP and the TSP . Our experimental findings highlight that PC-LSILS improves the smoothing performance of the HC transformation, and further improves the overall performance of the algorithm. Introduction COPs are a class of problems mainly to find an optimal combination to maximize or minimize some performance metrics with limited resources or subject to some constraints. COPs are typically categorized as NP-hard, for which classical optimization methods struggle to find the optimal solution within a reasonable amount of time and become less applicable. Consequently, researchers usually use heuristics or metaheuristics to find near-optimal solutions within a reasonable amount of time. One of the key challenges associated with solving COPs is the presence of numerous local optima in the solution space, primarily attributable to the rugged and irregular nature of their fitness landscapes. It can be hypothesized that smoothing the landscapes of COPs could significantly facilitate the attainment of the global optima.

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism integrates the proposed Node-Destroyer Model, a machine learning hybrid model that utilized Graph Neural Networks (GNNs) such identifies and selects customer nodes to guide the Large Neighborhood Search (LNS) operator within the metaheuristic optimization frameworks. This model leverages the structural properties of the problem and solution that can be represented as a graph, to guide strategic selections concerning node removal. The proposed approach reduces operational complexity and scales down the search space involved in the optimization process. The hybrid approach is applied specifically to the CVRP and does not require retraining across problem instances of different sizes. The proposed hybrid mechanism is able to improve the performance of baseline metaheuristic algorithms. Our approach not only enhances the solution quality for standard CVRP benchmarks but also proves scalability on very large-scale instances with up to 30,000 customer nodes. Experimental evaluations on benchmark datasets show that the proposed hybrid mechanism is capable of improving different baseline algorithms, achieving better quality of solutions under similar settings.

Bayesian optimization over the latent spaces of deep autoencoder models (DAEs) has recently emerged as a promising new approach for optimizing challenging black-box functions over structured, discrete, hard-to-enumerate search spaces (e.g., molecules). Here the DAE dramatically simplifies the search space by mapping inputs into a continuous latent space where familiar Bayesian optimization tools can be more readily applied. Despite this simplification, the latent space typically remains high-dimensional. Thus, even with a well-suited latent space, these approaches do not necessarily provide a complete solution, but may rather shift the structured optimization problem to a high-dimensional one. In this paper, we propose LOL-BO, which adapts the notion of trust regions explored in recent work on high-dimensional Bayesian optimization to the structured setting.

The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems and thus have a vast array of applications in machine learning, operations research, and many other fields. Choosing cutting planes effectively is a major research topic in the theory and practice of integer programming. We conduct a novel structural analysis of branch-and-cut that pins down how every step of the algorithm is affected by changes in the parameters defining the cutting planes added to the input integer program. Our main application of this analysis is to derive sample complexity guarantees for using machine learning to determine which cutting planes to apply during branch-and-cut.

Stochastic search algorithms are general black-box optimizers. Due to their ease of use and their generality, they have recently also gained a lot of attention in operations research, machine learning and policy search. Yet, these algorithms require a lot of evaluations of the objective, scale poorly with the problem dimension, are affected by highly noisy objective functions and may converge prematurely. To alleviate these problems, we introduce a new surrogate-based stochastic search approach. We learn simple, quadratic surrogate models of the objective function.