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Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
The optimal transmission switching problem (OTSP) is an established problem of changing a power grid's topology to obtain an improved operation by controlling the switching status of transmission lines. This problem was proven to be…
Spatial puzzles composed of rigid objects, flexible strings and holes offer interesting domains for reasoning about spatial entities that are common in the human daily-life's activities. The goal of this work is to investigate the automated…
I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…
Computing sets of high quality solutions has gained increasing interest in recent years. In this paper, we investigate how to obtain sets of optimal solutions for the classical knapsack problem. We present an algorithm to count exactly the…
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be very efficient in solving high dimensional problems. Even though…
Reasoning models represent a significant advance in LLM capabilities, particularly for complex reasoning tasks such as mathematics and coding. Previous studies confirm that parallel test-time compute-sampling multiple solutions and…
Heuristics in theorem provers are often parameterised. Modern theorem provers such as Vampire utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
We consider optimal planning in a large-scale system formalised as a hierarchical finite state machine (HFSM). A planning algorithm is proposed computing an optimal plan between any two states in the HFSM, consisting of two steps: A…
Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC)…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not extend trivially to Generalized Planning (GP). GP aims to compute algorithmic solutions that are valid for a set of…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be…