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This document introduces a set of 24 box-constrained numerical global optimization problem instances, systematically constructed using the Generalized Numerical Benchmark Generator (GNBG). These instances cover a broad spectrum of problem…
The evaluation of heuristic optimizers on test problems, better known as \emph{benchmarking}, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box…
Most optimization problems in real life applications are often highly nonlinear. Local optimization algorithms do not give the desired performance. So, only global optimization algorithms should be used to obtain optimal solutions. This…
Several Artificial Intelligence based heuristic and metaheuristic algorithms have been developed so far. These algorithms have shown their superiority towards solving complex problems from different domains. However, it is necessary to…
We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
The paper presents a collection of analytical benchmark problems specifically selected to provide a set of stress tests for the assessment of multifidelity optimization methods. In addition, the paper discusses a comprehensive ensemble of…
The domain of metaheuristic optimization has become vibrant due to a flood of new algorithms using a new nature-inspired metaphor but lacking clear methodological novelty. The Criticism behind the development of these algorithms has reached…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Complex engineering problems can be modelled as optimisation problems. For instance, optimising engines, materials, components, structure, aerodynamics, navigation, control, logistics, and planning is essential in aerospace. Metaheuristics…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value. That is all local optima are also global optima. This paper suggests that such functions are easily fortified by adding…
Modern optimisation algorithms are often metaheuristic, and they are very promising in solving NP-hard optimization problems. In this paper, we show how to use the recently developed Firefly Algorithm to solve nonlinear design problems. For…
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works…
The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimization algorithms. However, its global optimality is not clear and there has been no mathematical proof put forward. In this paper, a…
Solving a problem with a deep learning model requires researchers to optimize the loss function with a certain optimization method. The research community has developed more than a hundred different optimizers, yet there is scarce data on…
In this paper we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an algorithm of Bertsimas and Sim (2003)…