Gustavo Luís Soares

Interval Robust Multi-Objective Evolutionary Algorithm

Uncertainties are commonly present in optimization systems, and when they are considered in the design stage, the problem usually is called a robust optimization problem. Robust optimization problems can be treated as noisy optimization problems, as worst case minimization problems, or by considering the mean and standard deviation values of the objective and constraint functions. The worst case scenario is preferred when the effects of the uncertainties on the nominal solution are critical to the application under consideration. Based on this worst case scenario, we developed the [I]RMOEA (Interval Robust Multi-Objective Evolutionary Algorithm), a hybrid method that combines interval analysis techniques to deal with the uncertainties in a deterministic way and a multi-objective evolutionary algorithm. We introduce [I]RMOEA and illustrate it on three robust test functions based on the ZDT problems. The results show that [I]RMOEA is an adequate way of tackling robust optimization problems with evolutionary techniques taking advantage of the interval analysis framework.

Appraisal of Surrogate Modeling Techniques: A Case Study of Electromagnetic Device

Simulations are successfully utilized to reproduce the behavior of complex systems in many knowledge fields. The computational effort is a key factor when high-cost simulations are required in optimization, principally, if the system to be optimized operates under uncertain conditions. In this context, surrogate modeling is useful to alleviate the CPU time. Hence, this paper presents a methodology to assess three surrogate techniques based on genetic programming (GP), a radial basis function neural network (RBF-NNs), and universal Kriging. These techniques are used in this paper to obtain analytical optimization functions that are accurate, fast to evaluate and suitable for interval robust optimization. The experiments were performed in a robust version of the TEAM 22 problem. The results show that the surrogate models obtained are reliable and appropriate for interval robust methods. The methodology presented is flexible and extensible to other problems in diverse fields of interest.

A Surrogate Genetic Programming Based Model to Facilitate Robust Multi-Objective Optimization: A Case Study in Magnetostatics

A common drawback of robust optimization methods is the effort expended to compute the influence of uncertainties, because the objective and constraint functions must be re-evaluated many times. This disadvantage can be aggravated if time-consuming methods, such as boundary or finite element methods are required to calculate the optimization functions. To overcome this difficulty, we propose the use of genetic programming to obtain high-quality surrogate functions that are quickly evaluated. Such functions can be used to compute the values of the optimization functions in place of the burdensome methods. The proposal has been tested on a version of the TEAM 22 benchmark problem with uncertainties in decision parameters. The performance of the methodology has been compared with results in the literature, ensuring its suitability, significant CPU time savings and substantial reduction in the number of computational simulations.

Superlinear Speedup in a 3-D Parallel Conjugate Gradient Solver

This paper presents a computational performance analysis of a parallel implementation of a conjugate gradient (CG) solver using domain decomposition and distributed memory computers, applied to a 3-D finite element method problem. The results show a superlinear speedup, which is not usually expected. The analysis shows why and how it can happen.

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using Interval Analysis combined with Particle Swarm Optimization. A Set Inverter Via Interval Analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a Space Cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified Particle Swarm Optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100,000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.

A Genetic Algorithm for Multi-component Optimization Problems: The Case of the Travelling Thief Problem

Real-world problems are often composed of multiple interdependent components. In this case, benchmark problems that do not represent that interdependence are not a good choice to assess algorithm performance. In recent literature, a benchmark problem called Travelling Thief Problem (TTP) was proposed to better represent real-world multi-component problems. TTP is a combination of two well-known problems: 0-1 Knapsack Problem (KP) and the Travelling Salesman Problem (TSP). This paper presents a genetic algorithm-based optimization approach called Multi-Component Genetic Algorithm (MCGA) for solving TTP. It aims to solve the overall problem instead of each sub-component separately. Starting from a solution for the TSP component, obtained by the Chained Lin-Kernighan heuristic, the MCGA applies the evolutionary process (evaluation, selection, crossover, and mutation) iteratively using different basic operators for KP and TSP components. The MCGA was tested on some representative instances of TTP available in the literature. The comparisons show that MCGA obtains competitive solutions in 20 of the 24 TTP instances with 195 and 783 cities.

PID step response using genetic programming

This paper describes an algorithm that generates analytic functions for PID step response characteristics (i. e. rise time, overshoot, settling time, peak time and integral of time weighted absolute error) in an application of a third-order plant. The algorithm uses genetic programming for symbolic regressions and provides formal expressions composed of variables, constants, elementary operators and mathematical functions. Results show a good fitting between the desired and obtained step response for DC motor positioning problem.