Elizabeth F. Wanner

Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.

A dynamic multiobjective hybrid approach for designing Wireless Sensor Networks

The increase in the demand for Wireless Sensor Networks (WSNs) has intensified studies which aim to obtain energy-efficient solutions, since the energy storage limitation is critical in those systems. However, there are other aspects which usually must be ensured in order to provide an efficient design of WSNs, such as area coverage and network connectivity. This paper proposes a multiobjective hybrid approach for solving the Dynamic Coverage and Connectivity Problem (DCCP) in flat WSN subjected to node failures. It combines a multiobjective global on-demand algorithm (MGoDA), which improves the current DCCP solution using a Genetic Algorithm, with a local online algorithm (LoA), which is intended to restore the network coverage when one or more failures occur. The proposed approach is compared with an Integer Linear Programming (ILP) based approach and a similar mono-objective approach with regard to coverage, energy consumption and residual energy of the solution provided by each method. Results achieved for a test instance show that the hybrid approach presented can obtain good solutions with a considerably smaller computational cost than ILP. The multiobjective approach still provides a feasible method for extending WSNs lifetime with slight decreasing in the network mean coverage.

Constrained Optimization Based on Quadratic Approximations in Genetic Algorithms

An aspect that often causes difficulties when using Genetic Algorithms for optimization is that these algorithms operate as unconstrained search procedures and most of the real-world problems have constraints of different types. There is a lack of efficient constraint handling technique to bias the search in constrained search spaces toward the feasible regions. We propose a novel methodology to be coupled with a Genetic Algorithm to solve optimization problems with inequality constraints. This methodology can be seen as a local search operator that uses quadratic and linear approximations for both objective function and constraints. In the local search phase, these approximations define an associated problem with a quadratic objective function and quadratic and/or linear constraints that is solved using an LMI (linear matrix inequality) formulation. The solution of this associated problems is then re-introduced in the GA population.We test the proposed methodology with a set of analytical function and the results show that the hybrid algorithm has a better performancewhen compared to the same Genetic Algorithmwithout the proposed local search operator. The tests also suggest that the proposed methodology is at least equivalent, and sometimes better than other methods that have been reported recently in literature.

A new performance metric for multiobjective optimization: the integrated sphere counting

A large number of evolutionary algorithms for solving multiobjective optimization problems has been already developed. Several merit factors for comparing the outcomes of these algorithms have also been proposed. However, evaluating Pareto-surface sample sets is still considered an open problem, since the result of a multiobjective evolutionary algorithm is a collection of vectors forming a nondominated set, that can be viewed under rather different merit criteria. In this paper, we present a new performance metric: the Integrated Sphere Counting. This metric is motivated on two reasoning principles: (i) the Pareto-surface is an object that is to be described via sample sets, in a sense that is similar to the sampled function description in signal processing; and (ii) the resolution that is to be employed in the Pareto-surface sample set depends on the decision-making procedure resolution, instead of the surface structure itself. We test this metric with two benchmark problems: the 0/1 Knapsack Problem and ZDT number 6 test suite.

Multi-Objective Evolutionary Optimization of Biological Pest Control with Impulsive Dynamics in Soybean Crops

The biological pest control in agriculture, an environment-friendly practice, maintains the density of pests below an economic injury level by releasing a suitable quantity of their natural enemies. This work proposes a multi-objective numerical solution to biological pest control for soybean crops, considering both the cost of application of the control action and the cost of economic damages. The system model is nonlinear with impulsive control dynamics, in order to cope more effectively with the actual control action to be applied, which should be performed in a finite number of discrete time instants. The dynamic optimization problem is solved using the NSGA-II, a fast and trustworthy multi-objective genetic algorithm. The results suggest a dual pest control policy, in which the relative price of control action versus the associated additional harvest yield determines the usage of either a low control action strategy or a higher one.

A quality metric for multi-objective optimization based on Hierarchical Clustering Techniques

This paper presents the Hierarchical Cluster Counting (HCC), a new quality metric for nondominated sets generated by multi-objective optimizers that is based on hierarchical clustering techniques. In the computation of the HCC, the samples in the estimate set are sequentially grouped into clusters. The nearest clusters in a given iteration are joined together until all the data is grouped in only one class. The distances of fusion used at each iteration of the hierarchical agglomerative clustering process are integrated into one value, which is the value of the HCC for that estimate set. The examples show that the HCC metric is able to evaluate both the extension and uniformity of the samples in the estimate set, making it suitable as a unary diversity metric for multiobjective optimization.

An enhanced statistical approach for evolutionary algorithm comparison

This paper presents an enhanced approach for comparing evolutionary algorithm. This approach is based on three statistical techniques: (a) Principal Component Analysis, which is used to make the data uncorrelated; (b) Bootstrapping, which is employed to build the probability distribution function of the merit functions; and (c) Stochastic Dominance Analysis, that is employed to make possible the comparison between two or more probability distribution functions. Since the approach proposed here is not based on parametric properties, it can be applied to compare any kind of quantity, regardless the probability distribution function. The results achieved by the proposed approach have provided more supported decisions than former approaches, when applied to the same problems.

Feedback-Control Operators for Evolutionary Multiobjective Optimization

New operators for Multi-Objective Evolutionary Algorithms (MOEAs) are presented here, including one archive-set reduction procedure and two mutation operators, one of them to be applied on the population and the other one on the archive set. Such operators are based on the assignment of spheres to the points in the objective space, with the interpretation of a representative region. The main contribution of this work is the employment of feedback control principles (PI control) within the archive-set reduction procedure and the archive-set mutation operator, in order to achieve a well-distributed Pareto-set solution sample. An example EMOA is presented, in order to illustrate the effect of the proposed operators. The dynamic effect of the feedback control scheme is shown to explain a high performance of this algorithm in the task of Pareto-set covering.

Continuous-space embedding genetic algorithm applied to the Degree Constrained Minimum Spanning Tree Problem

This work presents an evolutionary approach for solving a difficult problem of combinatorial optimization, the DCMST (Degree-Constrained Minimum Spanning Tree Problem). Three genetic algorithms which embed candidate solutions in the continuous space [1] are proposed here for solving the DCMST. The results achieved by these three algorithms have been compared with four other existing algorithms according to three merit criteria: i) quality of the best solution found; ii) computational effort spent by the algorithm, and; iii) convergence tendency of the population. The three proposed algorithms have provided better results for both solution quality and population convergence, with reasonable computational cost, in tests performed for 25-node and 50-node test instances. The results suggest that the proposed algorithms are well suited for dealing with the problem under study.

Projection-based local search operator for multiple equality constraints within genetic algorithms

This paper presents a new operator for genetic algorithms that enhances convergence in the case of multiple nonlinear equality constraints. The proposed operator, named CQA-MEC (Constraint Quadratic Approximation for Multiple Equality Constraints), performs the steps: (i) the approximation of the non-linear constraints via quadratic functions; (ii) the determination of exact equality-constrained projections of some points onto the approximated constraint surface, via an iterative projection algorithm; and (iii) the re-insertion of the constraint- satisfying points in the genetic algorithm population. This operator can be interpreted both as a local search engine (that employs local approximations of constraint functions for correcting the feasibility) and a kind of elitism operator for equality constrained problems that plays the role of fixing the best estimates of the feasible set. The proposed operator has the advantage of not requiring any additional function evaluation per algorithm iteration, solely making usage of the information that is already obtained in the course of the usual genetic algorithm iterations. The test cases that were performed suggest that the new operator can enhance both the convergence speed (in terms of the number of function evaluations) and the accuracy of the final result.