The problem of denoising piecewise constant signals while preserving their jumps is a challenging problem that arises in many scientific areas. Several denoising algorithms exist such as total variation, convex relaxation, Markov random fields models, etc. The DPS algorithm is a combinatorial algorithm that excels the classical GNC in term of speed and SNR resistance. However, its running time slows down considerably for large signals. The main reason for this bottleneck is the size and the number of linear systems that need to be solved. We develop a recursive implementation of the DPS algorithm that uses the conditional independence, created by a confirmed discontinuity between two parts, to separate the reconstruction process of each part. Additionally, we propose an accelerated Cholesky solver which reduces the computational cost and memory usage. We evaluate the new implementation on a set of synthetic and real world examples to compare the quality of our solver. The results show a significant speed up, especially with a higher number of discontinuities.
In the decline phase of product lifecycle, industrials need to re-design their products to introduce new functions and/or customers’ new preferences. These changes may not only affect the product’s bill of material, but also its supply chain network. Consequently, new supply chain costs are generated. This paper addresses the problem of supply chain configuration considering new product re-design using a multi-agent system (MAS). The objective of the system is to ensure good collaboration between two different points of view, supply chain partners and product designers, to make better decisions. To model the proposed system, we select the multi-agent system engineering (MaSe) methodology. The MAS framework contains three types of agents, namely, “product design agent” and “supply chain agents” which are fitted with optimization tools. These tools allow costs’ optimization and selection of supply chain means (suppliers, technologies, etc.). Finally, the system contains a “communication agent” acting like a mediator; it facilitates data exchange between designers. To support distributed decision-making, two models of mixed integer linear programming are adopted and implemented within the framework for supply chain optimization. The overall MAS approach was tested in simulation with a case study. The objective of the simulation is to choose among three product alternatives the cheapest one based on its supplying and production costs, under capacity constraints. The MAS was able to find the best product alternative among three alternatives proposed by product design team and select optimal supply chain means. The optimal supply chain contains two suppliers: one machine and one subcontractor to satisfy customer’s demand.
The aim of this paper is to address the problem of supplier selection in a context of an integrated product design. Indeed, the product specificities and the suppliers’ constraints are both integrated into product design phase. We consider the case of improving the design of an existing product and study the selection of its suppliers adopting a bi-objective optimization approach. Considering multi-products, multi-suppliers and multi-periods, the mathematical model proposed aims to minimize supplying, transport and holding costs of product components as well as quality rejected items. To solve the bi-objective problem, an evolutionary algorithm namely, non-dominant sorting genetic algorithm (NSGA-II) is employed. The algorithm provides a set of Pareto front solutions optimizing the two objective functions at once. Since parameters values of genetic algorithms have a significant impact on their efficiency, we have proposed to study the impact of each parameter on the fitness functions in order to determine the optimal combination of these parameters. Thus, a number of simulations evaluating the effects of crossover rate, mutation rate and number of generations on Pareto fronts are presented. To evaluate performance of the algorithm, results are compared to those obtained by the weighted sum method through a numerical experiment. According to the computational results, the non-dominant sorting genetic algorithm outperforms the CPLEX MIP solver in both solution quality and computational time.
In this paper, we focus on the problem of change point detection in piecewise constant signals. This problem is central to several applications such as human activity analysis, speech or image analysis and anomaly detection in genetics. We present a novel window-sliding algorithm for an online change point detection. The proposed approach considers a local blanket of a global Markov Random Field (MRF) representing the signal and its noisy observation. For each window, we define and solve the local energy minimization problem to deduce the gradient on each edge of the MRF graph. The gradient is then processed by an activation function to filter the weak features and produce the final jumps. We demonstrate the effectiveness of our method by comparing its running time and several detection metrics with state of the art algorithms.
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