When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the de...
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When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resources, problems with the features above need to be linearized and then solved using solution algorithms for linear programming. The adaptive linear programming (ALP) algorithm is an extension of the Sequential linear programming algorithm where a nonlinear compromise decision support problem (cDSP) is iteratively linearized, and the resulting linear programming problem is solved with satisficing solutions returned. The reduced move coefficient (RMC) is used to define how far away from the boundary the next linearization is to be performed, and currently, it is determined based on a heuristic. The choice of RMC significantly affects the efficacy of the linearization process and, hence, the rapidity of finding the solution. In this paper, we propose a rule-based parameter-learning procedure to vary the RMC at each iteration, thereby significantly increasing the speed of determining the ultimate solution. To demonstrate the efficacy of the ALP algorithm with parameter learning (ALPPL), we use an industry-inspired problem, namely, the integrated design of a hot-rolling process chain for the production of a steel rod. Using the proposed ALPPL, we can incorporate domain expertise to identify the most relevant criteria to evaluate the performance of the linearization algorithm, quantify the criteria as evaluation indices, and tune the RMC to return the solutions that fall into the most desired range of each evaluation index. Compared with the old ALP algorithm using the golden section search to update the RMC, the ALPPL improves the algorithm by identifying the RMC values with better linearization performance without adding computational complexity. The insensitive region of the RMC is better explored using the ALPPL-the ALP
Based on the multi-objective linear weighted method and the characteristic that the sum of the weighted coefficients of the bi-objective function is 1, a weighted iteration algorithm for solving bi-objective linear op...
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Based on the multi-objective linear weighted method and the characteristic that the sum of the weighted coefficients of the bi-objective function is 1, a weighted iteration algorithm for solving bi-objective linear optimization has been proposed. The basic principle of the algorithm is that when the weighted coefficients increase gradually from a very small value to 1, an efficient solution can be obtained. The iteration algorithm needs convergence conditions. This paper proves the relationship between the iterative convergence conditions and the optimal solution of the objective function, and multiple efficient solutions can be obtained by iteration. According to the actual demand of the project, a method of determining the most efficient solution is given. The main advantage of the algorithm is that the implementation process of the weighted iteration algorithm only needs the optimal solution of a single objective function, and there is no complex process or algorithm for solving weighted coefficients. The algorithm is simple and effective, and overcomes the shortcomings of the existing algorithms that have the complex parameter setting and solving process. The examples and application show that the weighted iteration algorithm is scientific and correct, and it is easy to be used and programmed and can play an important role in practical engineering application.
Goal models are an effective mechanism for elicitation and analysis in early Requirements Engineering, improving communication with stakeholders. However, in real scenarios, goal models become a complex network of act...
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linear programming modeling is mainly concerned with solving the maximum or minimum value of a linear function under a group of linear constraints. It has been widely used in many subjects and fields. As an applicatio...
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Group discussions and assignments play a pivotal role in the classroom and online study. Existing research has mainly focused on exploring the educational impact of group learning, while the study on automated groupin...
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Group discussions and assignments play a pivotal role in the classroom and online study. Existing research has mainly focused on exploring the educational impact of group learning, while the study on automated grouping still remains under-explored. This paper proposes a principled method that aims to achieve personalized, accurate, and efficient grouping outcomes. Dubbed as Personas-based Student Grouping (PSG), our method first applies unsupervised clustering techniques to assign personas to students based on their behavioral characteristics. Based on their personas, we then utilize deep reinforcement learning to search for appropriate grouping rules and perform linear programming to obtain a suitable grouping scheme. Finally, the teaching effectiveness is fed back as the rewards to the reinforcement learning model to optimize future grouping scheme selections. Extensive experiments conducted on MOOCs datasets show that PSG can achieve more advantageous performance in both efficiency and effectiveness compared to the manual or random grouping mechanism. We hope PSG can provide students with a more enhanced learning experience and contribute to the future development of education. Our project homepage is available at https://***.
This paper intends to construct a new multi-dimensional preference analysis model for learners by using the improved linear programming method of multi-dimensional preference analysis (LINMAP) to get the weight vector...
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Machine learning methods for automatic classification problems using computational geometry are considered. Classes are defined by convex hulls of sets of points in a multidimensional feature space. The classification...
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Machine learning methods for automatic classification problems using computational geometry are considered. Classes are defined by convex hulls of sets of points in a multidimensional feature space. The classification algorithms based on the evaluation of the proximity of a test point to the convex hulls of classes are examined. A new method for proximity evaluation based on linear programming is proposed. The corresponding nearest convex hull classifier is described. The results of experimental studies on real problems of medical diagnostics are presented. The comparison of the effectiveness of the proposed classifier with the classifiers of other types has shown a sufficiently high efficiency of the proposed method for proximity evaluation based on linear programming.
The time–cost trade-off has been recognized as a very significant aspect of construction management. Generally, time–cost trade-off can be modeled as a fuzzy linear programming problem with symmetric or non-symmetri...
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We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider...
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We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the MongeKantorovich mass transfer problem. We also demonstrate a connection between the mass transfer problem and the dual linear variational problem. A numerical solution of the linear variational problem is also considered. The direct solution of this type of problem presents a huge computational complexity. To overcome this difficulty we use the so-called multiscale approach based on constructing a chain of approximations that are solutions on refining grids.
Full technical details for a slightly simplified version of the minimum weight perfect matching via blossom belief propagation by Ahn, Park, Chertkov and Shin (in Advances in neural information processing systems, vol...
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Full technical details for a slightly simplified version of the minimum weight perfect matching via blossom belief propagation by Ahn, Park, Chertkov and Shin (in Advances in neural information processing systems, vol 28, Curran Associates, Inc., 2015) are provided. An example showing the necessity of a certain uniqueness assumption is given. An alternative to perturbing the edge weights to ensure the uniqueness assumption is satisfied is suggested.
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