Dalarna University's logo and link to the university's website

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

The aim of this work is to propose a numerical method for solving different types of partial and ordinary differential equations. The equations share the same common property for their solutions to become infinite (blow up behaviour) or to become null (extinction behaviour) in finite time. This type of equations is solved using a sliced time computing technique, combined with rescaling both the variable time and the solution of the differential system. The main criterion under which the slice of time is defined, consists in imposing that the rescaled solution should not be greater than a preset cut off value. Another selection criterion for the method is based on the invariance and similarity conditions, enforced on the rescaled model in each of the time slices

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

In this paper, we present a new approach to simulate time-dependent initial value differential equations which solutions have a common property of blowing-up in a finite time. For that purpose, we introduce the concept of “sliced-time computations”, whereby, a sequence of time intervals (slices) {[Tn − 1, Tn]| n ≥ 1} is defined on the basis of a change of variables (re-scaling), allowing the generation of computational models that share symbolically or numerically “similarity” criteria. One of these properties is to impose that the re-scaled solution computed on each slice do not exceed a well-defined cut-off value (or threshold) S. In this work we provide fundamental elements of the method, illustrated on a scalar ordinary differential equation y′ = f(y) where f(y) verifies $\int_0^\infty {f(y)dy} < \infty$. Numerical results on various ordinary and partial differential equations are available in [7], some of which will be presented in this paper.

This dissertation is focused on theoretical and experimental studies of optical properties of materials and multilayer structures composing liquid crystal displays (LCDs) and electrochromic (EC) devices.

By applying spectroscopic ellipsometry, we have determined the optical constants of thin films of electrochromic tungsten oxide (WO_x) and nickel oxide (NiO_y), the films’ thickness and roughness. These films, which were obtained at spattering conditions possess high transmittance that is important for achieving good visibility and high contrast in an EC device.

Another application of the general spectroscopic ellipsometry relates to the study of a photo-alignment layer of a mixture of azo-dyes SD-1 and SDA-2. We have found the optical constants of this mixture before and after illuminating it by polarized UV light. The results obtained confirm the diffusion model to explain the formation of the photo-induced order in azo-dye films.

We have developed new techniques for fast characterization of twisted nematic LC cells in transmissive and reflective modes. Our techniques are based on the characteristics functions that we have introduced for determination of parameters of non-uniform birefringent media. These characteristic functions are found by simple procedures and can be utilised for simultaneous determination of retardation, its wavelength dispersion, and twist angle, as well as for solving associated optimization problems.

Cholesteric LCD that possesses some unique properties, such as bistability and good selective scattering, however, has a disadvantage – relatively high driving voltage (tens of volts). The way we propose to reduce the driving voltage consists of applying a stack of thin (~1µm) LC layers.

We have studied the ability of a layer of a surface stabilized ferroelectric liquid crystal coupled with several retardation plates for birefringent color generation. We have demonstrated that in order to accomplish good color characteristics and high brightness of the display, one or two retardation plates are sufficient.

Algorithms designed to solve dynamic multi-objective optimization problems (DMOPs) need to consider all of themultiple conflicting objectives to determine the optimal solutions. However, objective functions, constraints orparameters can change over time, which presents a considerable challenge. Algorithms should be able not only toidentify the optimal solution but also to quickly detect and respond to any changes of environment. In order toenhance the capability of detection and response to environmental changes, we propose a dynamic multiobjectiveoptimization (DMOO) algorithm based on the detection of environment change intensity andensemble learning (DMOO-DECI&EL). First, we propose a method for detecting environmental change intensity,where the change intensity is quantified and used to design response strategies. Second, a series of responsestrategies under the framework of ensemble learning are given to handle complex environmental changes.Finally, a boundary learning method is introduced to enhance the diversity and uniformity of the solutions.Experimental results on 14 benchmark functions demonstrate that the proposed DMOO-DECI&EL algorithmachieves the best comprehensive performance across three evaluation criteria, which indicates that DMOODECI&EL has better robustness and convergence and can generate solutions with better diversity compared tofive other state-of-the-art dynamic prediction strategies. In addition, the application of DMOO-DECI&EL to thereal-world scenario, namely the economic power dispatch problem, shows that the proposed method caneffectively handle real-world DMOPs.

The ’black box’ characteristics of Convolutional Neural Networks (CNNs) present significant risks to their application scenarios, such as reliability, security, and division of responsibilities. Addressing the interpretability of CNN emerges as an urgent and critical issue in the field of machine learning. Recent research on CNN interpretability has either yielded unstable or inconsistent interpretations, or produced coarse-scale interpretable heatmaps, limiting their applicability in various scenarios. In this work, we propose a novel method of CNNs interpretation by incorporating a joint evaluation of multiple feature maps and employing multi-objective optimization (JE&MOO-CAM). Firstly, a method of joint evaluation for all feature maps is proposed to preserve the complete object instances and improve the overall activation values. Secondly, an interpretation method of CNNs under the MOO framework is proposed to avoid the instability and inconsistency of interpretation. Finally, the operators of selection, crossover, and mutation, along with the method of population initialization in NSGA-II, are redesigned to properly express the characteristics of CNNs. The experimental results, including both qualitative and quantitative assessments along with a sanity check conducted on three classic CNN models—VGG16, AlexNet, and ResNet50—demonstrate the superior performance of the proposed JE&MOO-CAM model. This model not only accurately pinpoints the instances within the image requiring explanation but also preserves the integrity of these instances to the greatest extent possible. These capabilities signify that JE&MOO-CAM surpasses six other leading state-of-the-art methods across four established evaluation criteria.