To optimally solve hard optimization problems in real life, many methods were designed and tested. The metaheuristics proved to be the generally adequate techniques, while the exact traditional optimization mathematical methods are prohibitively expensive in computational time. The population-based metaheuristics, which manipulate a set of candidate solutions at a time, have advantages over the...

In recent years, the application of metaheuristic techniques to solve multi-objective optimization problems (MOPs) has become an active research area. Solving these kinds of problems involves obtaining a set of Pareto-optimal solutions in such a way that the corresponding Pareto front fulfills the requirements of convergence to the true Pareto front and uniform diversity. Most studies on metahe...

We define difficult optimization problems as problems which cannot be solved to optimality or to any guaranteed bound by any standard solver within a reasonable time limit. The problem class we have in mind are mixed integer programming (MIP) problems. Optimization and especially mixed integer optimization is often appropriate and frequently used to model real world optimization problems. While...

A key characteristic of Mixed-Integer (MI) problems is the presence of both continuous and discrete problem variables. These variables can interact in various ways, resulting in challenging optimization problems. In this paper, we study the design of an algorithm that combines the strengths of LTGA and iAMaLGaM: state-of-the-art model-building EAs designed for discrete and continuous search spa...

We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system that executes an analog computation. The systemindependent component of the equations of motion of this dynamical system can be integrated analytically for vari...

In this paper, we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of optimization problems for continuous and discrete variable optimization, particularly nonlinear an...

Optimization as an enabling technology has been one of the big success stories in process systems engineering. In this paper we present first a general review of optimization and its applications to a variety of problems in process systems engineering. Next, we provide an overview of two key areas: nonlinear programming and logic-based discrete/continuous optimization. In particular, recent adv...

Optimization of discrete structures aims at generating a new structure with the better property given an existing one, which is fundamental problem in machine learning. Different from continuous optimization, realistic applications optimization (e.g., text generation) are very challenging due to complex and long-range constraints, including both syntax semantics, structures. In this work, we pr...

Many real life optimization problems are nonconvex and may have several local minima within their feasible region. Therefore, global search methods are needed. Metaheuristics are efficient global optimizers including a metastrategy that guides a heuristic search. Genetic algorithms, simulated annealing, tabu search and scatter search are the most well-know metaheuristics. In general, they do no...