# Edite M.G.P. FernandesUniversity of Minho · ALGORITMI Research Centre

Edite M.G.P. Fernandes

Full Professor (retired)

## About

159

Publications

12,699

Reads

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1,249

Citations

Citations since 2017

Introduction

Additional affiliations

January 1990 - present

## Publications

Publications (159)

This paper analyzes an iterative kernel partitioning clustering algorithm that dynamically merges, removes and adds clusters using some characteristics, like the radii and diameters of the clusters, and distance between centers. The clustering is carried out in feature space in terms of a kernel function so that non-linearly separable clusters are...

Numerical direct multiple shooting (MS) methods have shown to be important and efficient tools to solve optimal control problems (OCP). The use of an MS method to solve the OCP gives rise to a finite-dimensional optimization problem with a set of “continuity constraints” that should be satisfied together with the other algebraic states and control...

In the present paper, we propose an iterative clustering approach that sequentially applies five processes, namely: the assign, delete, split, delete and optimization. It is based on the fitness probability scores of the cluster centers to identify the least fitted centers to undergo an optimization process, aiming to improve the centers from one i...

A direct multiple shooting (MS) method is implemented to solve optimal control problems (OCP) in the Mayer form. The use of an MS method gives rise to the so-called ‘continuity conditions’ that must be satisfied together with general algebraic equality and inequality constraints. The resulting finite nonlinear optimization problem is solved by a fi...

In this paper, we investigate the use of a simple heuristic in the DIRECT method context, aiming to select a set of the hyperrectangles that have the lowest function values in each size group. For solving bound constrained global optimization problems, the proposed heuristic divides the region where the hyperrectangles with the lowest function valu...

This paper contains a proposal to assign points to clusters, represented by their centers, based on weighted expected distances in a cluster analysis context. The proposed clustering algorithm has mechanisms to create new clusters, to merge two nearby clusters and remove very small clusters, and to identify points ‘noise’ when they are beyond a rea...

The optimal design of a single screw extrusion (SSE) is a very difficult task since it deals with several conflicting performance indices. Past research to find the optimal SSE design has been successfully conducted by optimization procedures, in particular by multi-objective optimization. Problems with two or more objectives have been addressed by...

This paper proposes a simplified version of the tabu search algorithm that solely uses randomly generated direction vectors in the exploration and intensification search procedures, in order to define a set of trial points while searching in the neighborhood of a given point. In the diversification procedure, points that are inside any already visi...

This paper is concerned with an extension of the heuristic DIRECT method, presented in [8], to solve nonlinear constrained global optimization (CGO) problems. Using a penalty strategy based on a penalty auxiliary function, the CGO problem is transformed into a bound constrained problem. We have analyzed the performance of the proposed algorithm usi...

This paper addresses the problem of solving a constrained global optimization problem using a modification of the DIRECT method that incorporates the filter methodology to simultaneously minimize the objective function and the constraints violation. Thus, in the “Selection” step of the herein proposed DIRECT-filter algorithm, the hyperrectangles ar...

This paper addresses the problem of solving a bound constrained global optimization problem by a population-based stochastic coordinate descent method. To improve efficiency, a small subpopulation of points is randomly selected from the original population, at each iteration. The coordinate descent directions are based on the gradient computed at a...

This paper presents a stochastic coordinate descent algorithm for solving bound constrained global optimization problems. The algorithm borrows ideas from some stochastic optimization methods available for the minimization of expected and empirical risks that arise in large-scale machine learning. Initially, the algorithm generates a population of...

This paper presents a DIRECT-type method that uses a filter methodology to assure convergence to a feasible and optimal solution of nonsmooth and nonconvex constrained global optimization problems. The filter methodology aims to give priority to the selection of hyperrectangles with feasible center points, followed by those with infeasible and non-...

This paper presents an experimental study that aims to compare the practical performance of well-known metaheuristics for solving the parameter estimation problem in a dynamic systems context. The metaheuristics produce good quality approximations to the global solution of a finite small-dimensional nonlinear programming problem that emerges from t...

A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) m...

This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an \(\varepsilon \)-global minimizer is proved. At each iteration k, the framework requires the \(\varepsilon ^{(k)}\)-global minimizer of a subpr...

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the...

An extension of the firefly algorithm (FA) for solving mixed-integer nonlinear programming (MINLP) problems is presented. Although penalty functions are nowadays frequently used to handle integrality conditions and inequality and equality constraints, this paper proposes the implementation within the FA of a simple rounded-based heuristic and four...

A practical comparison of penalty functions for globally solving mixed-integer nonlinear programming (MINLP) problems is presented. The penalty approach relies on the continuous relaxation of the MINLP problem by adding a specific penalty term to the objective function. A new penalty algorithm that addresses simultaneously the reduction of the erro...

In this paper, we consider a tumor growth mathematical model that includes an immune system and drug therapies. Immuno- and chemodrug administration as well as periodic administration of radiation are integrated in the model. We have set an optimal control (OC) problem relative to the model so that the average number of tumor cells and immuno- and...

This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are suf...

The problem herein addressed is a parameter estimation problem of the \(\alpha \)-pinene process. The state variables of this bioengineering process satisfy a set of differential equations and depend on a set of unknown parameters. A dynamic system based parameter estimation problem aiming to estimate the model parameter values in a way that the pr...

In this paper we compare the dynamics of three tumor growth models that include an immune system and a drug administration therapy using optimal control. The objective is to minimize a combined function of the total of tumor cells over time and a chemotherapeutic drug administration.

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A pe...

The BBMCSFilter method was developed to solve mixed integer nonlinear programming problems. This kind of problems have integer and continuous variables and they appear very frequently in process engineering problems. The objective of this work is to analyze the performance of the method when the coordinate searches are interrupted in the context of...

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an -global minimizer is proved. At each iteration k, the algorithm requires the -global minimization of a bound constrained optimization subproblem, where . The subp...

In this article, we aim to extend the firefly algorithm (FA) to solve bound constrained mixed-integer nonlinear programming (MINLP) problems. An exact penalty continuous formulation of the MINLP problem is used. The continuous penalty problem comes out by relaxing the integrality constraints and by adding a penalty term to the objective function th...

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0-1 multidimensional knapsack problems that are NP-hard. In the last decades, several exact as well as heurist...

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to en...

In this paper, we propose an extension of the firefly algorithm (FA) to multi-objective optimization. FA is a swarm intelligence optimization algorithm inspired by the flashing behavior of fireflies at night that is capable of computing global solutions to continuous optimization problems. Our proposal relies on a fitness assignment scheme that giv...

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in tu...

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an -global minimizer is guaranteed. At each iteration , the algorithm requires a -global minimizer of a bound constrained bi-objective subproblem, where as , gives the constraint violation tolerance and i...

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The mul...

A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictio...

A methodology for finding the optimal values of the decision variables from an efficient simplified mathematical model of an activated sludge system is addressed in this paper. The work herein presented arises in a wastewater treatment plant design context, where investment and operational costs are to be minimized and computational effort is to be...

This paper proposes a simplified binary version of the artificial fish swarm algorithm (S-bAFSA) for solving 0-1 quadratic knapsack problems. This is a combinatorial optimization problem, which arises in many fields of optimization. In S-bAFSA, trial points are created by using crossover and mutation. In order to make the points feasible, a random...

This paper aims to present a hyperbolic augmented Lagrangian (HAL) framework with guaranteed convergence to an @e-global minimizer of a constrained nonlinear optimization problem. The bound constrained subproblems that emerge at each iteration k of the framework are solved by an improved artificial fish swarm algorithm. Convergence to an @e^k-globa...

In this paper, the multi-objective formulation of an optimization problem arising from an activated sludge (AS) system of a wastewater treatment plant (WWTP) design optimization is solved through a multi-objective genetic algorithm. Two multi-objective approaches are proposed. First, a solution to the WWTP design is provided, regardless of its loca...

In this study, we propose an extended version of the Hooke and Jeeves
algorithm that uses a simple heuristic to handle integer and/or binary
variables and a filter set methodology to handle constraints. This
proposal is integrated into a multistart method as a local solver and it
is repeatedly called in order to compute different optimal solutions....

In this paper, we present a derivative-free multilevel coordinate search
(MCS) approach, that relies on the Hooke and Jeeves local search, for
globally solving bound constrained optimization problems. Numerical
experiments show that the proposed algorithm is effective in solving
benchmark problems, when compared with the well-known solvers MCS and...

This paper presents a differential evolution heuristic to compute a
solution of a system of nonlinear equations through the global
optimization of an appropriate merit function. Three different mutation
strategies are combined to generate mutant points. Preliminary numerical
results show the effectiveness of the presented heuristic.

Uncapacitated facility location problem (UFLP) is a combinatorial optimization problem, which has many applications. The artificial fish swarm algorithm has recently emerged in continuous optimization problem. In this paper, we present a simplified binary version of the artificial fish swarm algorithm (S-bAFSA) for solving the UFLP. In S-bAFSA, tri...

Multilocal programming aims to locate all the local solutions of an optimization problem. A stochastic method based on a multistart strategy and a derivative-free filter local search for solving general constrained optimization problems is presented. The filter methodology is integrated into a coordinate search paradigm in order to generate a set o...

Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satis...

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school....

This chapter aims to address the challenging and demanding issue of solving a continuous nonlinear constrained global optimization problem. We propose four stochastic methods that rely on a population of points to diversify the search for a global solution: genetic algorithm, differential evolution, artificial fish swarm algorithm and electromagnet...

The main goal of this paper is to analyze the behavior of nonmonotone hybrid tabu search approaches when solving systems of nonlinear inequalities and equalities through the global optimization of an appropriate merit function. The algorithm combines global and local searches and uses a nonmonotone reduction of the merit function to choose the loca...

Multilocal programming aims to identify all local maximizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local maximizers. Th...

Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading e...

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptiv...

This paper presents a derivative-free nonmonotone hybrid tabu search to
compute a solution of overdetermined systems of inequalities and
equalities through the global optimization of an appropriate merit
function. The proposed algorithm combines global and local searches
aiming to reduce computational effort. Preliminary numerical results
show the...

The multidimensional 0---1 knapsack problem is a combinatorial optimization problem, which is NP-hard and arises in many fields of optimization. Exact as well as heuristic methods exist for solving this type of problem. Recently, a population-based artificial fish swarm algorithm was proposed and applied in an engineering context. In this paper, we...

A stochastic global optimization method based on a multistart strategy and a derivative-free filter local search for general constrained optimization is presented and analyzed. In the local search procedure, approximate descent directions for the constraint violation or the objective function are used to progress towards the optimal solution. The a...

An artificial fish swarm algorithm based on a filter methodology for trial solutions acceptance is analyzed for general constrained global optimization problems. The new method uses the filter set concept to accept, at each iteration, a population of trial solutions whenever they improve constraint violation or objective function, relative to the c...

Hybridization of genetic algorithms with local search approaches can enhance their performance in global optimization. Genetic algorithms, as most population based algorithms, require a considerable number of function evaluations. This may be an important drawback when the functions involved in the problem are computationally expensive as it occurs...

This article presents a numerical study of two augmented Lagrangian algorithms to solve continuous constrained global optimization problems. The algorithms approximately solve a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors an...

In this article, we present a numerical study of three nonmonotone filter line search techniques, as well as a three-dimensional filter approach, when incorporated into the solver IPOPT, a primal-dual barrier method developed by Wächter and Biegler [On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear pr...

Semi-infinite programming (SIP) problems can be efficiently solved by reduction-type methods. Here, we present a new reduction method for SIP, where the multi-local optimization is carried out with a stretched simulated annealing algorithm, the reduced (finite) problem is approximately solved by a Newton's primal–dual interior point method that use...

Here we present a primal‐dual interior point method that relies on a filter line search method to promote global convergence of nonlinear optimization problems. Each entry in the filter includes two components directly taken from the first‐order optimality conditions of the problem. Primal feasibility, complementarity and dual feasibility measures...

The herein presented mutation-based artificial fish swarm (AFS) algorithm includes mutation operators to prevent the algorithm to falling into local solutions, diversifying the search, and to accelerate convergence to the global optima. Three mutation strategies are introduced into the AFS algorithm to define the trial points that emerge from rando...

This papers aims at providing a combined strategy for solving systems of equalities and inequalities. The combined strategy uses two types of steps: a global search step and a local search step. The global step relies on a tabu search heuristic and the local step uses a deterministic search known as Hooke and Jeeves. The choice of step, at each ite...

This paper presents a pattern search algorithm and its hybridization with a random descent search for solving bound constrained minimax problems. The herein proposed heuristic pattern search method combines the Hooke and Jeeves (HJ) pattern and exploratory moves with a randomly generated approximate descent direction. Two versions of the heuristic...

This paper carries out a numerical study of filter line search strategies that aim at minimizing the objective function and
the Karush-Kuhn-Tucker (KKT) vector error in order to encourage global convergence of interior point methods. These filter
strategies are implemented in an infeasible primal-dual interior point framework for nonlinear programm...

Engineering design optimization problems are formulated as large-scale mathematical programming problems with nonlinear objective
function and constraints. Global optimization finds a solution while satisfying the constraints. Differential evolution is
a population-based heuristic approach that is shown to be very efficient to solve global optimiza...

Semi-infinite programming (SIP) problems can be efficiently solved by reduction type methods. Here, we present a new reduction
method for SIP, where the multi-local optimization is carried out with a multi-local branch-and-bound method, the reduced
(finite) problem is approximately solved by an interior point method, and the global convergence is p...

The heuristics herein presented are modified versions of the artificial fish swarm algorithm for global optimization. The
new ideas aim to improve solution accuracy and reduce computational costs, in particular the number of function evaluations.
The modifications also focus on special point movements, such as the random, search and the leap moveme...

This paper presents an augmented Lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems. The method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm. A stochastic convergence analysis of the fish swarm...

A methodology to solve nonconvex constrained mixed-integer nonlinear programming (MINLP) problems is presented. A MINLP problem is one where some of the variables must have only integer values. Since in most applications of the industrial processes, some problem variables are restricted to take discrete values only, there are real practical problem...

In this paper, we analyze a possible way to implement a filter line search approach based on three measures in a primal‐dual interior point method for nonlinear programming. Two measures arise directly from the first order optimality conditions of the problem and the other is the barrier function. We solve a well‐known set of small and medium‐scale...

The task of global optimization is to find a point where the objective function obtains its most extreme value. Differential evolution (DE) is a population‐based heuristic approach that creates new candidate solutions by combining several points of the same population. The algorithm has three parameters: amplification factor of the differential var...

This paper aims to validate a proposed simplified model of the activated sludge system. A comparison between the classical and simplified models is made. The optimization of the operational and investment costs in order to achieve the best design is conducted using an augmented Lagrangian pattern search based algorithm. The results are similar in b...

Genetic algorithms as most population based algorithms are good at identifying promising areas of the search space (exploration), but less good at fine-tuning the approximation to the minimum (exploita-tion). Conversely, local search algorithms like pattern search are good at improving the accuracy of that approximation. Thus, a promising idea is c...

When modeling an activated sludge system of a wastewater treatment
plant (WWTP), several conflicting objectives may arise. The proposed formulation
is a highly constrained bi-objective problem where the minimization of the
investment and operation costs and the maximization of the quality of the effluent
are simultaneously optimized. These two conf...

This paper presents a numerical study of a stochastic augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vect...

We present a methodology to solve nonconvex Mixed-Integer Nonlinear
Programming problems, that combines the Branch-and-Bound and simulated
annealing type methods, which was implemented in MATLAB. A set of
benchmark functions with simple bounds and different dimensions was used
to analyze its practical behaviour. We exhibit computational results
sho...

In this paper, we present a new stochastic hybrid technique for constrained global optimization. It is a combination of the electromagnetism-like (EM) mechanism with a random local search, which is a derivative-free procedure with high ability of producing a descent direction. Since the original EM algorithm is specifically designed for solving bou...

Many optimization problems involve integer and continuous variables that can be modeled as mixed integer nonlinear programming (MINLP) problems. This has led to a wide range of applications, in particular in some engineering areas. Here, we provide a brief overview on MINLP, and present a simple idea for a future nonconvex MINLP solution technique.

This paper presents a new simulated annealing algorithm to solve constrained multi-global optimization problems. To compute all global solutions in a sequential manner, we combine the function stretching technique with the adaptive simulated annealing variant. Constraint-handling is carried out through a nondifferentiable penalty function. To bench...

In this paper, we present a new filter line search method based on two measures that is integrated into the primal-dual barrier method developed by Wa¨chter and Biegler [Mathematical Programming 106 (2006), pp. 25–57] for nonlinear programming. One measure arises directly from the first order optimality conditions of the problem and the other is th...

The algorithm herein presented is a modified version of the artificial fish swarm algorithm for global optimization. The new ideas are focused on a set of move-ments, closely related to the random, the searching and the leaping fish behaviors. An extension to bound constrained problems is also presented. To assess the per-formance of the new fish s...

We describe a reduction algorithm for solving semi-innite program-ming problems. The proposed algorithm uses the simulated annealing method equipped with a function stretching as a multi-local procedure, and a penalty tech-nique for the nite optimization process. An exponential penalty merit function is reduced along each search direction to ensure...

This paper presents an algorithm for solving global optimization problems with bounded variables. The algorithm is a modification of the electromagnetism-like mechanism proposed by Birbil and Fang [An electromagnetism-like mechanism for global optimization, J. Global Optim. 25 (2003), pp. 263-282]. The differences are mainly on the local search pro...

The Electromagnetism-like (EM) algorithm, developed by Birbil and Fang (J Global Optim 25(3):263–282, 2003) is a population-based
stochastic global optimization algorithm that uses an attraction-repulsion mechanism to move sample points towards optimality.
A typical EM algorithm for solving continuous bound constrained optimization problems perform...

1. Abstract A well-known approach for solving constrained optimization problems is based on penalty functions. A penalty technique transforms the constrained problem into an unconstrained problem by penalizing the objective function when constraints are violated and then minimizing the penalty function using meth-ods for unconstrained problems. In...

Here, we present some numerical experiments with a reduction method for solving nonlinear semi-infinite programming (SIP) problems. The method relies on a line search technique to ensure a sufficient decrease of a L2-exponential merit function. The proposed merit function is continuous for SIP and improves the algorithm efficiency when compared wit...

This paper introduces a modification on the movement force vector of the Birbil and Fang's electromagnetism-like algorithm [1] for solving global optimization problems with bounded variables. The proposed movement vector combines the total force exerted on each point of the population, at the current iteration, with the rate of change in the force...

This paper presents the implementation of a constraint-handling technique within the electromagnetism-like algorithm devised by Birbil and Fang, for solving real-world engineering design problems. A derivative-free elite-based descent search scheme is also included in the final stage of each iteration to accelerate convergence and improve accuracy....