Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses

The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise.We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise.We denote the resulting algorithm as vector fitting with adding and skimming (VF-AS). A thorough validation of the VF-AS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VF-AS algorithm to measured scattering responses of interconnect structures and networks typical of high-speed digital systems

Metaheuristics for black-box robust optimisation problems

Our interest is in the development of algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly (implementation uncertainty) the aim is to find a robust one. Here that is to find a point in the decision variable space such that the worst solution from within an uncertainty region around that point still performs well. This thesis comprises three research papers. One has been published, one accepted for publication, and one submitted for publication. We initially develop a single-solution based approach, largest empty hypersphere (LEH), which identifies poor performing points in the decision variable space and repeatedly moves to the centre of the region devoid of all such points. Building on this we develop population based approaches using a particle swarm optimisation (PSO) framework. This combines elements of the LEH approach, a local descent directions (d.d.) approach for robust problems, and a series of novel features. Finally we employ an automatic generation of algorithms technique, genetic programming (GP), to evolve a population of PSO based heuristics for robust problems. We generate algorithmic sub-components, the design rules by which they are combined to form complete heuristics, and an evolutionary GP framework. The best performing heuristics are identified. With the development of each heuristic we perform experimental testing against comparator approaches on a suite of robust test problems of dimension between 2D and 100D. Performance is shown to improve with each new heuristic. Furthermore the generation of large numbers of heuristics in the GP process enables an assessment of the best performing sub-components. This can be used to indicate the desirable features of an effective heuristic for tackling the problem under consideration. Good performance is observed for the following characteristics: inner maximisation by random sampling, a small number of inner points, particle level stopping conditions, a small swarm size, a Global topology, and particle movement using a baseline inertia formulation augmented by LEH and d.d. capabilities

A constraint programming approach for the premarshalling problem

[EN] The enormous amount of containers handled at ports hampers the efficiency of terminal operations. The optimization of crane movements is crucial for speeding up the loading and unloading of vessels. To this end, the premarshalling problem aims to reorder a set of containers placed in adjacent stacks with a minimum number of crane movements, so that a container with an earlier retrieval time is not below one with a later retrieval time. In this study, we present a series of constraint programming models to optimally solve the premarshalling problem. Extensive computational comparisons show that the best proposed constraint programming formulation yields better results than the state-of-the-art integer programming approach. A salient finding in this paper is that the logic behind the model construction in constraint programming is radically different from that of more traditional mixed integer linear programming models.Acknowledgements This study has been partially supported by the Spanish Ministry of Science and Innovation under predoctoral grant PRE2019-087706 and the project 'OPTEP-Port Terminal Operations Opti-mization' (No. RTI2018-094940-B-I00) financed with FEDER funds.Jiménez-Piqueras, C.; Ruiz, R.; Parreño-Torres, C.; Alvarez-Valdes, R. (2023). A constraint programming approach for the premarshalling problem. European Journal of Operational Research. 306(2):668-678. https://doi.org/10.1016/j.ejor.2022.07.042668678306

Optimizing pre-processing and relocation moves in the Stochastic Container Relocation Problem

In container terminals, containers are often moved to other stacks in order to access containers that need to leave the terminal earlier. We propose a new optimization model in which the containers can be moved in two different phases: a pre-processing and a relocation phase. To solve this problem, we develop an optimal branch-and-bound algorithm. Furthermore, we develop a local search heuristic because the problem is NP-hard. Besides that, we give a rule-based method to estimate the number of relocation moves in a bay. The local search heuristic produces solutions that are close to the optimal solution. Finally, for instances in which the benefits of moving containers in the two different phases are in balance, the solution of the heuristic yields significant improvement compared to the existing methods in which containers are only moved in one of the two phases