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A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop…
A variety of strategies have been proposed for overcoming local optimality in metaheuristic search. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from a local optimum…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…
A fundamental challenge in neurosymbolic systems is applying continuous gradient-based optimization to discrete logical domains. While fuzzy relaxations provide differentiability, they often lack a formal structural alignment with classical…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
Slow self-avoiding adaptive walks by an infinite radius search algorithm (Limax) are analyzed as themselves, and as the network they form. The study is conducted on several NK problems and two HIFF problems. We find that examination of such…
Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In…
Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This…
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…
One of the most critical issues in machine learning is the selection of appropriate hyper parameters for training models. Machine learning models may be able to reach the best training performance and may increase the ability to generalize…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…
In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there…
Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…
We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic…
Dynamic maneuvers for legged robots present a difficult challenge due to the complex dynamics and contact constraints. This paper introduces a versatile trajectory optimization framework for continuous-time multi-phase problems. We…