The fight against forgery of valuable items demands efficient and reasonably priced solutions. A security tag featuring holographic elements for anti-counterfeiting is one of them. However, the content and colours of a diffraction image that would be seen by an observer are often counterintuitive in the design stage. Here, we propose an original algorithm based on the conical diffraction formalism, which can be used to describe the variations of a diffraction image with respect to all aspects of observation. We validate the output of the algorithm by comparing it to test holograms, which we have produced by employing direct laser interference patterning (DLIP) in electrochemically grown nickel foil. We have employed a motorized femtosecond laser system to micro-machine arrays of 65 µm × 65 µm sized diffraction gratings with a defined orientation and pitch on the order of 1 µm. Based on completed diffraction efficiency measurements, we determined optimal ablation parameters, i.e. 57.4 mJ/cm2 fluence per pulse and 1100 pulses/pixel. Furthermore, we show how accurate the proposed algorithm is through measured diffraction spectra as well as captured diffraction images of test holograms produced using the obtained parameters. Finally, we showcase anti-counterfeiting tag prototypes with complex holographic effects, i.e. colour reconstruction, animation effects, and image multiplexing. The proposed algorithm can severely shorten the time between design and production of a holographic tag, especially when realizing it via a competitive origination technology—DLIP.

Given an edge-weighted undirected graph with weights specifying dissimilarities between pairs of objects, represented by the vertices of the graph, the clique partitioning problem (CPP) is to partition the vertex set of the graph into mutually disjoint subsets such that the sum of the edge weights over all cliques induced by the subsets is as small as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. The proposed algorithm incorporates tabu search, local search, and solution perturbation procedures. We report computational results on CPP instances of size up to 2000 vertices. Performance comparisons of ITS against state-of-the-art methods from the literature demonstrate the competitiveness of our approach.

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The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.

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