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Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
We provide the global optimization community with new optimality proofs for six deceptive benchmark functions (five bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are…
The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions.…
This paper addresses the Flexible Job Shop Scheduling Problem and its extension with Worker Flexibility, which integrates workforce assignment into machine-operation scheduling. Diverse solvers have been proposed across multiple…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still unsatisfactory understood and characterized. For this reason, the selection of…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
We present our latest contributions in terms of mathematical modeling and algorithm development for the global optimization of the ACOPF problem. These contributions allow us to close the optimality gap on a number of open instances in the…
Recently, there has been much work on the design of general heuristics for graph-based, combinatorial optimization problems via the incorporation of Graph Neural Networks (GNNs) to learn distribution-specific solution structures.However,…
This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input…
Benchmarking is a key aspect of research into optimization algorithms, and as such the way in which the most popular benchmark suites are designed implicitly guides some parts of algorithm design. One of these suites is the black-box…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
We develop algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly the aim is to find a robust one, where the worst case in an…
GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More' and Toraldo, this algorithm was designed for large-scale problems but had been…
Research on new optimization algorithms is often funded based on the motivation that such algorithms might improve the capabilities to deal with real-world and industrially relevant optimization challenges. Besides a huge variety of…
When applying machine learning to problems in NLP, there are many choices to make about how to represent input texts. These choices can have a big effect on performance, but they are often uninteresting to researchers or practitioners who…
In this article we combine two developments in polynomial optimization. On the one hand, we consider nonnegativity certificates based on sums of nonnegative circuit polynomials, which were recently introduced by the second and the third…