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Da Silva, C., Peces, M., Faundez, M., Hansen, H., Campos, J. L., Dosta, J., et al. (2022). Gamma distribution function to understand anaerobic digestion kinetics: Kinetic constants are not constant. Chemosphere, 306, 135579.
Abstract: The Gamma model is a novel approach to characterise the complex degradation dynamics taking place during anaerobic digestion. This three parameters model results from combining the firstorder kinetic model and the Gamma distribution function. In contrast to conventional models, where the kinetic constant is considered invariant, the Gamma model allows analysing the variability of the kinetic constant using a probability density function. The kinetic constant of monodigestion and codigestion batch tests of different wastes were modelled using the Gamma model and two common firstorder models: onestep onefraction model and onestep twofraction model. The Gamma distribution function approximates three distinct probability density functions, i.e. exponential, lognormal, and delta Dirac. Specifically, (i) cattle paunch and pig manure approximated a lognormal distribution; (ii) cattle manure and microalgae approximated an exponential distribution, and (iii) primary sludge and cellulose approximated a delta Dirac distribution. The Gamma model was able to characterise two distinct waste activated sludge, one approximated to a lognormal distribution and the other to an exponential distribution. The same cellulose was tested with two different inocula; in both tests, the Gamma distribution function approximated a delta Dirac function but with a different kinetic value. The potential and consistency of Gamma model were also evident when analysing pig manure and microalgae codigestion batch tests since (i) the mean k of the codigestion tests were within the values of the monodigestion tests, and (ii) the profile of the density function transitioned from lognormal to exponential distribution as the percentage of microalgae in the mixture increased.

MunozHerrera, S., & Suchan, K. (2022). Constrained Fitness Landscape Analysis of Capacitated Vehicle Routing Problems. Entropy, 24(1), 53.
Abstract: Vehicle Routing Problems (VRP) comprise many variants obtained by adding to the original problem constraints representing diverse system characteristics. Different variants are widely studied in the literature; however, the impact that these constraints have on the structure of the search space associated with the problem is unknown, and so is their influence on the performance of search algorithms used to solve it. This article explores how assignation constraints (such as a limited vehicle capacity) impact VRP by disturbing the network structure defined by the solution space and the local operators in use. This research focuses on Fitness Landscape Analysis for the multiple Traveling Salesman Problem (mTSP) and Capacitated VRP (CVRP). We propose a new Fitness Landscape Analysis measure that provides valuable information to characterize the fitness landscape's structure under specific scenarios and obtain several relationships between the fitness landscape's structure and the algorithmic performance.
