A novel algorithm to allocate customers and retailers in a closed-loop supply chain under probabilistic demand

In this paper, a closed-loop supply chain (CLSC) is modeled to obtain the best location of retailers and allocate them to other utilities. The structure of CLSC includes production centers, retailers’ centers, probabilistic customers, collection, and disposal centers. In this research, two strategies are considered to find the best location for retailers by focusing on 1- the type of expected movement 2- expected coverage (distance and time) for minimizing the costs and maximizing the profit by considering the probabilistic customer and uncertainly demand. First of all, the expected distances between customers and retailers are calculated per movement method. These values are compared with the Maximum expected coverage distance of retailers, which is displayed in algorithm 1 heuristically, and the minimum value is picked. Also, to allocate customers to retailers, considering the customer's movement methods and comparing it with Maximum expected coverage time, which is presented in Algorithm 2 heuristically, the minimum value is chosen to this end, a bi-objective nonlinear programming model is proposed. This model concurrently compares Strategies 1 and 2 to select the best competitor. Based on the chosen strategy, the best allocation is determined by employing two heuristic algorithms, and the locations of the best retailers are determined. As the proposed model is NP-hard, a meta-heuristics (non-dominated sorting genetic) algorithm is employed for the solution process. Afterward, the effectiveness of the proposed model is validated and confirmed, and the obtained results are analyzed. For this purpose, a numerical example is given and solved through the optimization software.

Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches

In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called potential-driven network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones (“looping”). The paper introduces a new mixed-integer nonlinear programming model and a new nonlinear programming model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations to practitioners about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models with respect to computational time, the number of solutions found, the number of instances solved and cost savings. Moreover, the paper extends the models for optimizing over multiple demand scenarios and is the first to include the practically relevant option that a particular pipeline may be looped several times.

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Traditional CCRMs (Constrained Center-and-Range Methods) in solving the problem of interval regression could hardly make tradeoffs between the overall fitting accuracy and the coincidence degree between the observed and predicted intervals and could also hardly reduce the number of disjoint elements between the observed and predicted intervals, as well as raise the average ratio of all predicted intervals contained within their observed intervals. This paper constructed a nonlinear regression model based on center-and-range method, in which the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval was incorporated into the traditional CCRM model’s objective. This novel nonlinear programming model was proven to be a convex one that satisfied K-T condition. Monte Carlo simulation shows that the model is degenerated to the compared CCRM+ model as the objective only contains the minimization of the overall fitting accuracy for both center and range sample series. In this situation, it could obtain a better solution than the use of the compared CCRM model. In addition, when the proposed model only takes into account the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval, the model shows a better performance than the CCRM+ model in terms of the average ratio of all predicted intervals contained within their observed intervals, as well as the average number of forecasts with 0% accuracy.

An Improved Crow Search Algorithm Applied to the Phase Swapping Problem in Asymmetric Distribution Systems

This paper discusses the power loss minimization problem in asymmetric distribution systems (ADS) based on phase swapping. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage consists of an improved version of the crow search algorithm. This stage is based on the generation of candidate solutions using a normal Gaussian probability distribution. The master stage is responsible for providing the connection settings for the system loads using integer coding. The slave stage uses a power flow for ADSs based on the three-phase version of the iterative sweep method, which is used to determine the network power losses for each load connection supplied by the master stage. Numerical results on the 8-, 25-, and 37-node test systems show the efficiency of the proposed approach when compared to the classical version of the crow search algorithm, the Chu and Beasley genetic algorithm, and the vortex search algorithm. All simulations were obtained using MATLAB and validated in the DigSILENT power system analysis software.