Traditional methods for detection of lead ions in water samples are costly and time-consuming. In this work, an accurate smartphone-based colorimetric sensor was developed utilizing a novel machine learning algorithm. In the presence of Pb 2+ ions in the solution of specifically functionalized gold nanoparticles, the color of solution turns from red to purple. Indeed, the color variation of the solution is proportional to Pb 2+ concentration. The smartphone camera captures the corresponding color change, and the image is processed by an efficient artificial intelligence protocol. The nonlinear regression approach was used for concentration estimation, in which the parameters of the proposed model are obtained using a new feature extraction algorithm. In prediction of Pb 2+ concentration, the average absolute error and root-mean-square error were 0.094 and 0.124, respectively. The influence of pH of the medium, temperature, oligonucleotide concentration, and reaction time on the performance of the proposed sensor was carefully investigated and understood to achieve the best sensor response. This novel sensor exhibited good linearity for the detection of Pb 2+ in the concentration range of 0.5–2000 ppb with a detection limit of 0.5 ppb.

The Gravitational Search Algorithm (GSA) has been proposed for solving continues problems based on the law of gravity. In this paper, we propose a Cognitive Discrete GSA (called CDGSA) for solving 0-1 knapsack problem. The GSA has used a function of time to determine the number of the best particles for attracting others in each time, while our main idea is based on attracting each particle with two cognitive and social components. The cognitive component contains the best position of the particles up to now, while the social component contains the particle with the best position in the whole of the system at the current time and the particles with the best position in the neighborhood. In the other words, the cognitive component is such an appropriate actuator for embedding in the intelligent agents like robots. Such intelligent agent or robot is guided in the right direction with the help of its best previous position. Finally, by introducing discrete version of this idea, the efficiency of the proposed algorithm is measured for 0-1 knapsack problem. Experimental results on some benchmark and high dimensional problems illustrate that the proposed algorithm has gained the better accuracy in comparison of the other similar methods.

The 0-1 knapsack problem is one of the classic NP-hard problems. It is an open issue in discrete optimization problems, which plays an important role in the real applications. Therefore, several algorithms have been developed to solve it. The Gravitational Search Algorithm (GSA) is an optimization algorithm based on the law of gravity and mass interactions. In the GSA, the searcher agents are a collection of masses that interact with each other based on the Newtonian gravity and the laws of motion. In this algorithm the position of the agents can be considered as the solutions. The GSA is a nature-inspired algorithm that is used for finding the optimum value of continuous functions. This paper introduces a Discrete version of the GSA (DGSA) for solving 0-1 knapsack problem. In this regard, we introduce an approach for discretely updating the position of each agent. In addition, a fitness function has been proposed for 0-1 knapsack problem. Our experimental results show the effectiveness of the DGSA in comparison with other similar algorithms in terms of the accuracy and overcoming the defect of local convergence.

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