Considerations of Accuracy and Uncertainty with Kriging Surrogate Models in Single-Objective Electromagnetic Design Optimization

The high computational cost of evaluating objective functions in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After briefly reviewing how such considerations have been made in the single-objective optimization of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim to maximize the accuracy of the initial surrogate model, from which the optimization search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined using experimental designs which yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through searching for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations may be achieved by starting the iterative optimization search earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimal design are discussed

A hybrid heuristic solving the traveling salesman problem

This paper presents a new hybrid heuristic for solving the Traveling Salesman Problem, The algorithm is designed on the frame of a general optimization procedure which acts upon two steps, iteratively. In first step of the global search, a feasible tour is constructed based on insertion approach. In the second step the feasible tour found at the first step, is improved by a local search optimization procedure. The second part of the paper presents the performances of the proposed heuristic algorithm, on several test instances. The statistical analysis shows the effectiveness of the local search optimization procedure, in the graphical representation.peer-reviewe

Strip Planarity Testing of Embedded Planar Graphs

In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $\gamma:V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each edge is monotone in the $y$-direction and, for any $u,v\in V$ with $\gamma(u)<\gamma(v)$, it holds $y(u)<y(v)$. The problem has strong relationships with some of the most deeply studied variants of the planarity testing problem, such as clustered planarity, upward planarity, and level planarity. We show that the problem is polynomial-time solvable if $G$ has a fixed planar embedding.Comment: 24 pages, 12 figures, extended version of 'Strip Planarity Testing' (21st International Symposium on Graph Drawing, 2013

Fuzzy Adaptive Tuning of a Particle Swarm Optimization Algorithm for Variable-Strength Combinatorial Test Suite Generation

Combinatorial interaction testing is an important software testing technique that has seen lots of recent interest. It can reduce the number of test cases needed by considering interactions between combinations of input parameters. Empirical evidence shows that it effectively detects faults, in particular, for highly configurable software systems. In real-world software testing, the input variables may vary in how strongly they interact, variable strength combinatorial interaction testing (VS-CIT) can exploit this for higher effectiveness. The generation of variable strength test suites is a non-deterministic polynomial-time (NP) hard computational problem \cite{BestounKamalFuzzy2017}. Research has shown that stochastic population-based algorithms such as particle swarm optimization (PSO) can be efficient compared to alternatives for VS-CIT problems. Nevertheless, they require detailed control for the exploitation and exploration trade-off to avoid premature convergence (i.e. being trapped in local optima) as well as to enhance the solution diversity. Here, we present a new variant of PSO based on Mamdani fuzzy inference system \cite{Camastra2015,TSAKIRIDIS2017257,KHOSRAVANIAN2016280}, to permit adaptive selection of its global and local search operations. We detail the design of this combined algorithm and evaluate it through experiments on multiple synthetic and benchmark problems. We conclude that fuzzy adaptive selection of global and local search operations is, at least, feasible as it performs only second-best to a discrete variant of PSO, called DPSO. Concerning obtaining the best mean test suite size, the fuzzy adaptation even outperforms DPSO occasionally. We discuss the reasons behind this performance and outline relevant areas of future work.Comment: 21 page

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics