Exact distributional analysis of online algorithms with lookahead

In online optimization, input data is revealed sequentially. Optimization problems in practice often exhibit this type of information disclosure as opposed to standard offline optimization where all information is known in advance. We analyze the performance of algorithms for online optimization with lookahead using a holistic distributional approach. To this end, we first introduce the performance measurement method of counting distribution functions. Then, we derive analytical expressions for the counting distribution functions of the objective value and the performance ratio in elementary cases of the online bin packing and the online traveling salesman problem. For bin packing, we also establish a relation between algorithm processing and the Catalan numbers. The paper shows that an exact analysis is strongly interconnected to the combinatorial structure of the problem and algorithm under consideration. Results further indicate that the value of lookahead heavily relies on the problem itself. The analysis also shows that exact distributional analysis could be used in order to discover key effects and identify related root causes in relatively simple problem settings. These insights can then be transferred to the analysis of more complex settings where the introduced performance measurement approach has to be used on an approximative basis (e.g., in a simulation-based optimization)

A matheuristic for customized multi-level multi-criteria university timetabling

Course timetables are the organizational foundation of a university’s educational program. While students and lecturers perceive timetable quality individually according to their preferences, there are also collective criteria derived normatively such as balanced workloads or idle time avoidance. A recent challenge and opportunity in curriculum-based timetabling consists of customizing timetables with respect to individual student preferences and with respect to integrating online courses as part of modern course programs or in reaction to flexibility requirements as posed in pandemic situations. Curricula consisting of (large) lectures and (small) tutorials further open the possibility for optimizing not only the lecture and tutorial plan for all students but also the assignments of individual students to tutorial slots. In this paper, we develop a multi-level planning process for university timetabling: On the tactical level, a lecture and tutorial plan is determined for a set of study programs; on the operational level, individual timetables are generated for each student interlacing the lecture plan through a selection of tutorials from the tutorial plan favoring individual preferences. We utilize this mathematical-programming-based planning process as part of a matheuristic which implements a genetic algorithm in order to improve lecture plans, tutorial plans, and individual timetables so as to find an overall university program with well-balanced timetable performance criteria. Since the evaluation of the fitness function amounts to invoking the entire planning process, we additionally provide a proxy in the form of an artificial neural network metamodel. Computational results exhibit the procedure’s capability of generating high quality schedules

Simulation-based multi-criteria decision making: an interactive method with a case study on infectious disease epidemics

Whenever a system needs to be operated by a central decision making authority in the presence of two or more conflicting goals, methods from multi-criteria decision making can help to resolve the trade-offs between these goals. In this work, we devise an interactive simulation-based methodology for planning and deciding in complex dynamic systems subject to multiple objectives and parameter uncertainty. The outline intermittently employs simulation models and global sensitivity analysis methods in order to facilitate the acquisition of system-related knowledge throughout the iterations. Moreover, the decision maker participates in the decision making process by interactively adjusting control variables and system parameters according to a guiding analysis question posed for each iteration. As a result, the overall decision making process is backed up by sensitivity analysis results providing increased confidence in terms of reliability of considered decision alternatives. Using the efficiency concept of Pareto optimality and the sensitivity analysis method of Sobol’ sensitivity indices, the methodology is then instantiated in a case study on planning and deciding in an infectious disease epidemic situation similar to the 2020 coronavirus pandemic. Results show that the presented simulation-based methodology is capable of successfully addressing issues such as system dynamics, parameter uncertainty, and multi-criteria decision making. Hence, it represents a viable tool for supporting decision makers in situations characterized by time dynamics, uncertainty, and multiple objectives

Comparison of different approaches to multistage lot sizing with uncertain demand

We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands

Optical differential reflectance spectroscopy for photochromic molecules on solid surfaces

Optical reflectance of thin adsorbates on solid surfaces is able to reveal fundamental changes of molecular properties compared to bulk systems. The detection of very small changes in the optical reflectance required several technical improvements in the past decades. We present an experimental setup that is capable of high-quality measurements of submonolayers and ultrathin layers of photochromic molecules on surfaces as well as quantifying their isomerization kinetics. By using photomultipliers as detectors, an enhancement of the signal-to-noise ratio by a factor of three with a total reduction of light exposure on the sample by at least four orders of magnitude is achieved. The potential of the experimental setup is demonstrated by a characterization of the photoswitching and thermal switching of a spirooxazine derivate on a bismuth surface

Effect of ligand methylation on the spin-switching properties of surface-supported spin-crossover molecules

X-ray absorption spectroscopy investigations of the spin-state switching of spin-crossover (SCO) complexes adsorbed on a highly-oriented pyrolytic graphite (HOPG) surface have shown so far that HOPG is a promising candidate to realize applications such as spintronic devices because of the stability of SCO complexes on HOPG and the possibility of highly efficient thermal and light-induced spin-state switching. Herein, we present the spin switching of several Fe(II) SCO complexes adsorbed on an HOPG surface with particular emphasis on the thermally induced spin transition behaviour with respect to different structural modifications. The complexes of the type [Fe(bpz)2(L)] (bpz  =  dihydrobis(pyrazolyl)borate, L  =  1,10-phenanthroline, 2,2'-bipyridine) and their methylated derivatives exhibit SCO in the solid state with some differences regarding cooperative effects. However, in the vacuum-deposited thick films on quartz, complete and more gradual spin transition behavior is observable via UV/vis spectroscopy. In contrast to that, all complexes show large differences upon direct contact with HOPG. Whereas the unmodified complexes show thermal and light-induced SCO, the addition of e.g. two or four methyl groups leads to a partial or a complete loss of the SCO on the surface. The angle-dependent measurement of the N K-edge compared to calculations indicates that the complete SCO and HS-locked molecules on the surface exhibit a similar preferential orientation, whereas complexes undergoing an incomplete SCO exhibit a random orientation on the surface. These results are discussed in the light of molecule-substrate interactions

Reversible Switching of Spiropyran Molecules in Direct Contact With a Bi(111) Single Crystal Surface

Photochromic molecular switches immobilized by direct contact with surfaces typically show only weak response to optical excitation, which often is not reversible. In contrast, here, it is shown that a complete and reversible ring-opening and ring-closing reaction of submonolayers of spironaphthopyran on the Bi(111) surface is possible. The ring opening to the merocyanine isomer is initiated by ultraviolet light. Switching occurs in a two-step process, in which after optical excitation, an energy barrier needs to be overcome to convert to the merocyanine form. This leads to a strong temperature dependence of the conversion efficiency. Switching of the merocyanine isomer back to the closed form is achieved by a temperature increase. Thus, the process can be repeated in a fully reversible manner, in contrast to previously studied nitrospiropyran molecules on surfaces. This is attributed to the destabilization of the merocyanine isomer by the electron-donating nature of the naphtho group and the reduced van der Waals interaction of the Bi(111) surface. The result shows that molecules designed for switching in solutions need to be modified to function in direct contact with a surface