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Concept: Mathematical optimization


The requirements of micronutrients for biomass and hydrocarbon production in Botryococcus braunii UTEX 572 were studied using response surface methodology. The concentrations of four micronutrients (iron, manganese, molybdenum, and nickel) were manipulated to achieve the best performance of B. braunii in laboratory conditions. The responses of algal biomass and hydrocarbon to the concentration variations of the four micronutrients were estimated by a second order quadratic regression model. Genetic algorithm calculations showed that the optimal level of micronutrients for algal biomass were 0.266 µM iron, 0.707 µM manganese, 0.624 µM molybdenum and 3.38 µM nickel. The maximum hydrocarbon content could be achieved when the culture media contained 10.43 µM iron, 6.53 µM manganese, 0.012 µM molybdenum and 1.73 µM nickel. The validation through an independent test in a photobioreactor suggests that the modified media with optimised concentrations of trace elements can increase algal biomass by 34.5% and hydrocarbon by 27.4%. This study indicates that micronutrients play significant roles in regulating algal growth and hydrocarbon production, and the response surface methodology can be used to optimise the composition of culture medium in algal culture.

Concepts: Algae, Photosynthesis, Metal, Agar, Mathematical optimization, Algae fuel, Algaculture, Botryococcus braunii


In this study, the siderophore-producing characteristics and conditions of Bacillus sp. PZ-1 were investigated and the enhancement of siderophores on Pb uptake and translocation in Brassica juncea were determined. Results of single factor experiment showed that glucose, pH and Pb(NO3)2 could stimulate PZ-1 growth and siderophore production. The maximum siderophore production of 90.52% siderophore units was obtained by response surface methodology optimization at glucose concentration of 21.84 g/l, pH 6.18 and Pb(NO3)2 concentration of 245.04 μmol/l. The type of siderophore was hydroxamate and its concentration in the fermentation broth amounted to 32.24 μg/ml. Results of pot experiment indicated that the siderophores enhanced Brassica juncea to assimilate more Pb from soil with the uptake ratio from 1.04 to 2.74 and translocate more Pb from underground to overground with the TF values from 1.21 to 1.48. The results revealed that Bacillus sp. PZ-1 could produce abundant siderophores and might be potentially used to augment the phytoextraction of Pb from soil.

Concepts: Enzyme, Operations research, Response surface methodology, Mathematical optimization, Hydroxamic acid, Phytoremediation, Brassica juncea, Siderophore


Chitin extraction from shrimp shells by biological treatment, using the Bacilli Bacillus pumilus A1, is a non-polluting method and offers the opportunity to preserve the exceptional qualities of chitin and its derivatives. However, the major disadvantage of the fermentative way is the low efficiency of demineralization and deproteinization. The aim of this study is to improve the yield of extraction which depends on many factors, such as the medium composition and the physical parameters. In order to look for the optimal conditions, a Plackett and Burman design was carried out to screen eight factors influencing the deproteinization and demineralization efficiencies. The four most influencing variables were then examined to achieve the optimization using a central composite design. The results obtained showed that the optimal conditions were: shrimp shell concentration of 70g/l, glucose concentration of 50g/l, pH of 5.0 incubated with 0.225 OD of B. pumilus A1 inoculum, at 35°C and 150rpm for 6 days in 500ml flask containing 100ml of working volume. These conditions led to 88% of demineralization and 94% of deproteinization. (13)C CP/MAS-NMR spectral analysis of the chitin prepared was carried out and was found to be similar to that of the commercial α-chitin.

Concepts: Quality, Quality control, Operations research, Bacillus, Response surface methodology, Mathematical optimization, Factorial experiment, Central composite design


The Polyhydroxybutyrate (PHB) producer, Bacillus licheniformis MSBN12 was isolated from the marine sponge Callyspongia diffusa. The PHB production of B. licheniformis MSBN12 was optimized using a four-factor Box-Behnken design to find the interactive effects of variables such as palm jaggery, wheat bran, seawater, and incubation temperature. The maximum yield of PHB (6.38 g/L) was achieved through response surface methodology-based optimization and the optimized conditions were further used for the batch and fed-batch fermentation. Maximum biomass was reached at 48 and 36 h of incubation with PHB accumulation of 62.91 and 67.16 % (w/w of dry cells) for batch and fed-batch process. The production of PHB under fed-batch process with B. licheniformis MSBN12 was increased threefold over shake flask culture when palm jaggery as sole carbon source. The ¹H NMR data was extrapolated with peaks of the PHB reference standard and confirmed as PHB analog.

Concepts: Wheat, Computer program, Maize, Bran, Mathematical optimization, Chaff, Bacillus licheniformis, Fed-batch


In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class © is present, along with the susceptible (S), the infected (I) and the removed ® ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin’s Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.

Concepts: Epidemiology, Infectious disease, Mathematics, Optimization, Introduction, Epidemic, Optimal control, Mathematical optimization


ABSTRACT. Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

Concepts: Algorithm, Cancer, Medical imaging, Genetic algorithm, Optimization, Mathematical optimization, Conjugate gradient method, Optimization algorithms


Hemicelluloses from sugarcane bagasse were subjected to microwave-assisted acid hydrolysis at mild temperature to produce xylooligosaccharides (XOS). The hydrolysis was performed with dilute H2SO4 at 90°C and the influence of acid concentration (0.1-0.3M) and reaction time (20-40min) on the XOS production was ascertained with response surface methodology based on central composite design. The fitted models of XOS and xylose yields were in good agreement with the experimental results. Compared to hydrolysis time, acid concentration was a more significant coefficient in the production of XOS. A well-defined degree of polymerisation of XOS and the monomer in the hydrolysates were quantified. No sugar-degraded byproduct was detected. The maximum XOS yield of 290.2mgg(-1) was achieved by hydrolysis with 0.24M H2SO4 for 31min. The results indicated that the yields of xylose and the byproducts can be controlled by the acid concentration and reaction time in microwave-assisted acid hydrolysis.

Concepts: Experimental design, Polymer, Polymer chemistry, Response surface methodology, Mathematical optimization, Factorial experiment, Central composite design, Bagasse


We propose a new archive-based steady-state micro genetic algorithm (ASMiGA). In this context, a new archive maintenance strategy is proposed, which maintains a set of nondominated solutions in the archive unless the archive size falls below a minimum allowable size. It makes the archive size adaptive and dynamic. We have proposed a new environmental selection strategy and a new mating selection strategy. The environmental selection strategy reduces the exploration in less probable objective spaces. The mating selection increases searching in more probable search regions by enhancing the exploitation of existing solutions. A new crossover strategy DE-3 is proposed here. ASMiGA is compared with five well-known multiobjective optimization algorithms of different types—generational evolutionary algorithms (SPEA2 and NSGA-II), archive-based hybrid scatter search, decomposition-based evolutionary approach, and archive-based micro genetic algorithm. For comparison purposes, four performance measures (HV, GD, IGD, and GS) are used on 33 test problems, of which seven problems are constrained. The proposed algorithm outperforms the other five algorithms.

Concepts: Algorithm, Genetic algorithm, Mathematical optimization, Evolutionary algorithm, Optimization algorithms, Evolutionary programming, Crossover, Genetic algorithms


This paper presents a novel collective neurodynamic optimization method for solving nonconvex optimization problems with bound constraints. First, it is proved that a one-layer projection neural network has a property that its equilibria are in one-to-one correspondence with the Karush-Kuhn-Tucker points of the constrained optimization problem. Next, a collective neurodynamic optimization approach is developed by utilizing a group of recurrent neural networks in framework of particle swarm optimization by emulating the paradigm of brainstorming. Each recurrent neural network carries out precise constrained local search according to its own neurodynamic equations. By iteratively improving the solution quality of each recurrent neural network using the information of locally best known solution and globally best known solution, the group can obtain the global optimal solution to a nonconvex optimization problem. The advantages of the proposed collective neurodynamic optimization approach over evolutionary approaches lie in its constraint handling ability and real-time computational efficiency. The effectiveness and characteristics of the proposed approach are illustrated by using many multimodal benchmark functions.

Concepts: Artificial intelligence, Problem solving, Neural network, Optimization, Constraint satisfaction, Mathematical optimization, Neural networks, Optimization problem


Natural arches, pillars and other exotic sandstone formations have always been attracting attention for their unusual shapes and amazing mechanical balance that leave a strong impression of intelligent design rather than the result of a stochastic process. It has been recently demonstrated that these shapes could have been the result of the negative feedback between stress and erosion that originates in fundamental laws of friction between the rock’s constituent particles. Here we present a deeper analysis of this idea and bridge it with the approaches utilized in shape and topology optimisation. It appears that the processes of natural erosion, driven by stochastic surface forces and Mohr-Coulomb law of dry friction, can be viewed within the framework of local optimisation for minimum elastic strain energy. Our hypothesis is confirmed by numerical simulations of the erosion using the topological-shape optimisation model. Our work contributes to a better understanding of stochastic erosion and feasible landscape formations that could be found on Earth and beyond.

Concepts: Mathematics, Mass, Force, Sandstone, Classical mechanics, Mathematical optimization, Stochastic, Intelligent design