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Hundreds of variants of Swarm Intelligence or Evolutionary Algorithms are proposed each year and numerous competitions and comparisons between algorithms may suggest rapid improvement in the field. However, such comparisons are often done between a limited number of methods and are based on averaged ranks of algorithms. This way they measure whether one method is on average ranked better than the others, without giving any information on how much improvement is in fact obtained. In this study we show a general comparison between 69 algorithms, starting from methods proposed in the 1960’s up to variants developed in the early 2020’s, on single-objective static numerical problems. Algorithms are compared on searching for a minimum of 30 different 50-dimensional mathematical functions, and on 22 real-world problems. We focus on the relative improvement achieved by various algorithms over a single-solution based method proposed in 1960 by Howard Rosenbrock. We find that the general improvement of Evolutionary Algorithms over Rosenbrock’s algorithm is relatively limited. It is high for the artificial benchmarks, for which many Evolutionary Algorithms find solutions 10 times closer to the global optimum in terms of fitness than Rosenbrock’s algorithm, but much lower for real-world problems. Improvement is also higher when performance averaged over many runs is compared, but lower when the best results from multiple runs are analyzed. In the last case, only the best Evolutionary Algorithms are able to find solutions of a “typical” real-world problem that are 2–3 times better in terms of fitness than those found by Rosenbrock’s algorithm. The relative improvement of recently proposed algorithms is not much better than the improvement achieved by algorithms proposed over a decade ago.

The air2water model is a simple and efficient tool for modeling surface water temperature in lakes based solely on the air temperature. In this article, we propose to modify the air2water model in such a way that different parameters would be associated with lake stratification of cold waters than with lake stratification of warm waters. The situation of a mix of both cold water and warm water is also considered. The model is tested on 22 lowland Polish lakes against two classical air2water variants. As the new air2water model variant is slightly more complicated than the basic versions, we focus on the importance of the choice of the calibration method. Each variant of the air2water model is calibrated with eight different optimization methods, which are also compared on various benchmark problems. We show that the proposed variant is superior to the classical air2water models on about 90% of tested lakes, but only if the calibration approach is properly selected, which confirms the importance of the links between the model and appropriate optimization procedures. The proposed air2water variant performs well on various lowland lakes, with exception of large but shallow ones, probably due to the weak stratification of the shallow lakes.

We report a detailed study of vector modulation instability (VMI) in highly birefringent fibers with circularly polarized modes in the normal dispersion regime. We show that because of suppression of coherent terms, the VMI in circularly birefringent fibers is governed by one set of coupled-mode nonlinear Schrödinger equations regardless of the fiber birefringence. In consequence, the VMI sidebands are polarized linearly and orthogonally to the pump up to the birefringence level of 10-5, similarly like in isotropic fibers. For greater birefringence the polarization states of the sidebands become elliptical with opposite handedness while the azimuth angle deviates from orthogonality to the pump. We also point on the dependence of the critical power beyond which the VMI cannot exist upon ellipticity angle θ of the eigenmodes. We show that the critical power gradually increases with the ellipticity angle and for θ > 17.6° the VMI gain is not limited, in contrast to linearly birefringent fibers. Our findings were confirmed experimentally by observation of the isotropic-like VMI in the spun side-hole fiber with nearly circularly polarized eigenmodes, in spite of relatively high birefringence of the order of 2 × 10-6.