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As humans, we hear sound every second of our life. The sound we hear is often affected by the acoustics of the environment surrounding us. For example, a spacious hall leads to more reverberation. Room Impulse Responses (RIR) are commonly…

In the (1-dimensional) bin packing problem, we are asked to pack all the given items into bins, each of capacity one, so that the number of non-empty bins is minimized. Zhu~[Chaos, Solitons \& Fractals 2016] proposed an approximation…

When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…

The ultimate goal of all optimization methods is to solve real-world problems. For a successful project execution, knowledge about optimization and the application has to be pooled. As it is too inefficient to highly train one person in…

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…

We consider a repeated auction where the buyer's utility for an item depends on the time that elapsed since his last purchase. We present an algorithm to build the optimal bidding policy, and then, because optimal might be impractical, we…

We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at…

We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…

This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs…

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…

We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…

The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…

Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…

Many circumstances of practical importance have performance or success metrics which exist implicitly---in the eye of the beholder, so to speak. Tuning aspects of such problems requires working without defined metrics and only considering…

In this study, we investigate optimal control problems that involve sweeping processes with a drift term and mixed inequality constraints. Our goal is to establish necessary optimality conditions for these problems. We address the…

In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of…

Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…

We propose a new iterative procedure to optimize the restart for meta-heuristic algorithms to solve combinatorial optimization, which uses independent algorithm executions. The new procedure consists of either adding new executions or…

We consider the problem of fairly and efficiently allocating indivisible items (goods or bads) under capacity constraints. In this setting, we are given a set of categorized items. Each category has a capacity constraint (the same for all…