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Recoverable robust optimization is a popular multi-stage approach, in which it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We consider recoverable robust optimization in combination with…
This paper presents a brand new methodology to deal with isotopic fine structure calculations. By using the Poisson approximation in an entirely novel way, we introduce mathematical elegance into the discussion on the trade-off between…
We present two novel applications of symmetries for mixed-integer linear programming. First we propose two variants of a new heuristic to improve the objective value of a feasible solution using symmetries. These heuristics can use either…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
In this article we demonstrate how to solve a variety of problems and puzzles using the built-in SAT solver of the computer algebra system Maple. Once the problems have been encoded into Boolean logic, solutions can be found (or shown to…
Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using…
A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO, which in itself is a potentially difficult and expensive task. State-of-the-art transformations from MAX-3SAT to…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
Layout synthesis is mapping a quantum circuit to a quantum processor. SWAP gate insertions are needed for scheduling 2-qubit gates only on connected physical qubits. With the ever-increasing number of qubits in NISQ processors, scalable…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…
In this paper, we report the use of rational Triangular Bezier Splines (rTBS) to numerically solve the von Karman equations, a system of fourth order PDEs. $C^{1}$ smoothness of the mesh, generated by triangular Bezier elements, enables us…