Almost all real-world problems have constraints. Constraint-handling is an important part of algorithm implementation in optimization. This chapter introduces the main techniques for handling constraints.
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Injectable Hydrogels In article number 2206554, Lin Yu and co-workers develop an injectable and thermosensitive hydrogel with inherent long-acting NO-releasing capacity. The hydrogel system loaded with β-lapachone and CuCys nanoparticles can synchronously boost intracellular reactive oxygen species and reactive nitrogen species levels, thereby synergistically enhancing the anti-tumor efficacy. This hydrogel is suitable as a platform for extending NO-associated medical applications.
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All metaheuristic optimization algorithms require some initialization, and the initialization for such optimizers is usually carried out randomly. However, initialization can have some significant influence on the performance of such algorithms. This paper presents a systematic comparison of 22 different initialization methods on the convergence and accuracy of five optimizers: differential evolution (DE), particle swarm optimization (PSO), cuckoo search (CS), artificial bee colony (ABC) and genetic algorithm (GA). We have used 19 different test functions with different properties and modalities to compare the possible effects of initialization, population sizes and the numbers of iterations. Rigorous statistical ranking tests indicate that 43.37% of the functions using the DE algorithm show significant differences for different initialization methods, while 73.68% of the functions using both PSO and CS algorithms are significantly affected by different initialization methods. The simulations show that DE is less sensitive to initialization, while both PSO and CS are more sensitive to initialization. In addition, under the condition of the same maximum number of fitness evaluations (FEs), the population size can also have a strong effect. Particle swarm optimization usually requires a larger population, while the cuckoo search needs only a small population size. Differential evolution depends more heavily on the number of iterations, a relatively small population with more iterations can lead to better results. Furthermore, ABC is more sensitive to initialization, while such initialization has little effect on GA. Some probability distributions such as the beta distribution, exponential distribution and Rayleigh distribution can usually lead to better performance. The implications of this study and further research topics are also discussed in detail.
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All mathematical models and differential equations we have discussed so far are deterministic systems in the sense that, for given initial and boundary conditions, the solutions of the system can be determined. There is no intrinsic randomness in differential equations. In reality, randomness occurs everywhere, and not all models are deterministic. In fact, it is necessary to use stochastic models and sometimes the only sensible models are stochastic descriptions. In these cases, we have to deal with probability and statistics.
The complicated mechanisms governing hydrocarbon expulsion (primary migration) have not as yet been fully understood, though understanding these mechanisms is paramount in basin modeling. This paper presents (a) a simple oil-expulsion model based on the principles of sedimentary compaction and the flow difference between oil and water, and (b) a simple gas-expulsion model via mass balance. These two models do not consider more factors or mechanisms than some existing models, but we verify that the predicated expelled amount is proper by using it as input data for secondary migration and confirming that the modeled volume of accumulated hydrocarbons is close to that determined by exploration. The hydrocarbon migration–accumulation (secondary migration) history is the most important component in basin modeling, but it is also one of the most challenging to achieve. In general, a sectional 2-D simulator cannot predict the amount of hydrocarbon accumulated, whereas a 3-D simulator takes considerable computing time. This paper presents a simplified pseudo 3-D model based on the principles of buoyancy drive and Darcy's Law in combination with the effects of faulting and lithology on migration pathways. Comparing with the existing four models currently in use (multi-phase Darcy flow, flowpath, hybrid method combining the former two approaches together, and invasion percolation), the proposed model is mainly targeted at calculating the quantities and locations of petroleum accumulations for oil and gas assessment, and so the factors taken into account and the functions needed to be executed in software are less than in other models. Application of the aforementioned three models in the Kuqa Depression of the Tarim Basin in western China shows that the simplified pseudo 3-D model is very efficient and less computationally extensive, and the predicted quantities and locations of petroleum accumulations approach those determined by exploration, showing these models could form a useful prospecting method.
Passive-cooling building materials can achieve cooling without external energy consumption, which is an energy-saving and environmentally friendly cooling method. However, the existing passive-cooling building materials have the limitations of high cost, complicated processes, and a toxic organic solvent, which hinders the passive-cooling technology applied in practical building. To overcome these limitations, we developed a facile, high-efficiency, non-toxic, and superhydrophobic passive-cooling building coating (SPCBC) with an efficient cooling capability and excellent durability that was composed of polydimethylsiloxane and SiO2. The fabricated SPCBC demonstrated a high reflectance and a high emittance, showing a superior cooling capability with a 14 °C temperature drop compared with a bare cement surface on a hot summer day. In addition, the SPCBC could not be wetted or contaminated by muddy water, corrosive aqueous solutions, or dust, which presented an excellent anti-fouling and self-cleaning capability. Moreover, the fabricated SPCBC could work outdoors for 30 days, withstand UV irradiation for 30 days, and resist accelerated aging for 100 h without any significant changes in the superhydrophobicity and the cooling capability, meaning that the SPCBC had an outstanding durability. This work provides a new method to facilitate passive-cooling technology to apply in practical building in hot weather regions of the world.
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This chapter introduces the essence of the finite difference method for solving ordinary different equations. It starts with the Euler scheme, followed by the analysis of numerical stability. Then higher-order methods are also covered, including the leap-frog and Runge–Kutta methods for initial value problems. The shooting method is then introduced for solving two-point boundary problems.
