Showing papers on "Linear programming published in 2022"

Novel L1 Regularized Extreme Learning Machine for Soft-Sensing of an Industrial Process

Abstract: Extreme learning machine (ELM) is suitable for nonlinear soft sensor development Yet it faces an overfitting problem To overcome it, this work integrates bound optimization theory with variational Bayesian (VB) inference to derive novel L1 norm-based ELMs An L1 term is attached to the squared sum cost of prediction errors to formulate an objective function Considering the nonconvexity and nonsmoothness of the objective function, this article uses bound optimization theory, and constructs a proper surrogate function to equivalently convert a challenging L1 norm-based optimization problem into easy one Then, VB inference is adopted for optimizing the converted problem Thus, an L1 norm-based ELM can be efficiently optimized by an alternating optimization algorithm with a proved convergence Finally, a soft sensor is developed based on the proposed algorithm An industrial case study is carried out to demonstrate that the proposed soft sensor is competitive against recent ones

Multiobjective U-Shaped Disassembly Line Balancing Problem Considering Human Fatigue Index and an Efficient Solution

Abstract: The progress of science and technology speeds up the replacement of products and produces a large number of end-of-life products. Traditional incineration causes a waste of resources and pollution to the environment. Disassembling and recycling end-of-life products are the recommended way to maximize the utilization of resources and reduce environmental pollution. Disassembly performance is affected by many factors, such as the disassembly posture of the human body, the fatigue of workers on a workstation, disassembly profit, and task precedence relationship. In this article, a mixed integer linear programming mathematical model for U-shaped layout disassembly line balancing problems is developed, in which the balance of workers’ fatigue indices is an optimization objective in addition to disassembly profits. An efficient solution to the problem that uses a collaborative resource allocation strategy of the multiobjective evolutionary algorithm is proposed. The linear programming solver CPLEX is used to verify the accuracy of the model and compared with the proposed algorithm. Experiments demonstrate that the algorithm is significantly superior to the CPLEX solver in handling large-scale cases. The proposed algorithm is also compared with two well-known algorithms, which further verifies its superiority.

Electric Bus Charging Scheduling for a Single Public Transport Route Considering Nonlinear Charging Profile and Battery Degradation Effect

Abstract: • A mixed-integer non-linear and nonconvex programming (MINL&NCP) model, which captures the unique feature of the EBCS problem is developed. We further approximate it by two novel MILP models in a smart way. • Non-linear charging profile and battery degradation effect are considered. • Three tailored valid inequalities are proposed to enhance the solution efficiency. • Extensive numerical experiments are carried out to seek valuable managerial insights for the public transport operators. This study deals with a fundamental electric bus charging scheduling (EBCS) problem for a single public transport route by considering the nonlinear electric bus (EB) charging profile and battery degradation effect under the partial charging policy, which allows EBs to be charged any length of time and make good use of dwell times between consecutive trips. Given a group of trip tasks for an EB fleet and charger type, the problem is to minimize the total cost for a public transport operator of providing peak-hour bus services for a focal single public transport route by simultaneously determining the EB-to-trip assignment and EB charging schedule with charger type choice subject to the necessary EB operational constraints. We first build a mixed-integer nonlinear and nonconvex programming (MINL&NCP) model for the EBCS problem. To effectively solve the MINL&NCP model to global optimality, we subsequently develop two mixed-integer linear programming (MILP) models by means of linearization and approximation techniques. To accelerate the solution efficiency, we further create three families of valid inequalities depending on the unique features of the problem. A real case study based on the No.171 bus route in Singapore is conducted to demonstrate the performance of the developed models. Extensive numerical experiments are carried out to seek valuable managerial insights for public transport operators.

A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: An interactive possibilistic programming approach for a real case study

Abstract: In uncertain circumstances like the COVID-19 pandemic, designing an efficient Blood Supply Chain Network (BSCN) is crucial. This study tries to optimally configure a multi-echelon BSCN under uncertainty of demand, capacity, and blood disposal rates. The supply chain comprises blood donors, collection facilities, blood banks, regional hospitals, and consumption points. A novel bi-objective Mixed-Integer Linear Programming (MILP) model is suggested to formulate the problem which aims to minimize network costs and maximize job opportunities while considering the adverse effects of the pandemic. Interactive possibilistic programming is then utilized to optimally treat the problem with respect to the special conditions of the pandemic. In contrast to previous studies, we incorporated socio-economic factors and COVID-19 impact into the BSCN design. To validate the developed methodology, a real case study of a Blood Supply Chain (BSC) is analyzed, along with sensitivity analyses of the main parameters. According to the obtained results, the suggested approach can simultaneously handle the bi-objectiveness and uncertainty of the model while finding the optimal number of facilities to satisfy the uncertain demand, blood flow between supply chain echelons, network cost, and the number of jobs created.

Operation of a Technical Virtual Power Plant Considering Diverse Distributed Energy Resources

Abstract: Virtual power plants (VPPs) have emerged as a way to coordinate and control the growing number of distributed energy resources (DERs) within power systems. Typically, VPP models have focused on financial or commercial outcomes and have not considered the technical constraints of the distribution system. The objective of this article is the development of a technical VPP (TVPP) operational model to optimize the scheduling of a diverse set of DERs operating in a day-ahead energy market, considering grid management constraints. The effects on network congestion, voltage profiles, and power losses are presented and analyzed. In addition, the thermal comfort of the consumers is considered and the tradeoffs between comfort, cost, and technical constraints are presented. The model quantifies and allocates the benefits of the DER operation to the owners in a fair and efficient manner using the Vickrey–Clarke–Grove mechanism. This article develops a stochastic mixed-integer linear programming model and various case studies are thoroughly examined on the IEEE 119 bus test system. Results indicate that electric vehicles provide the largest marginal contribution to the TVPP, closely followed by solar photovoltaic (PV) units. Also, the results show that the operations of the TVPP improve financial metrics and increase consumer engagement while improving numerous technical operational metrics. The proposed TVPP model is shown to improve the ability of the system to incorporate DERs, including those from commercial buildings.

Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

Abstract: We provide a comprehensive overview of the literature of algorithmic approaches for multiobjective mixed-integer and integer linear optimization problems. More precisely, we categorize and display exact methods for multiobjective linear problems with integer variables for computing the entire set of nondominated images. Our review lists 108 articles and is intended to serve as a reference for all researchers who are familiar with basic concepts of multiobjective optimization and who have an interest in getting a thorough view on the state-of-the-art in multiobjective mixed-integer programming.

Transactive Energy Management of V2G-Capable Electric Vehicles in Residential Buildings: An MILP Approach

Abstract: This paper proposes a new energy management model for residential buildings to handle the uncertainties of demand and on-site PV generation. For this purpose, the building energy management system (BEMS) organizes a transactive energy (TE) market among plug-in electric vehicles (PEVs) to determine their charge/discharge scheduling. According to the proposed TE framework, the PEV owners get reimbursed by the BEMS for the flexibility they offer. In this regard, the PEV owners submit their response curves for reimbursement upon arrival. Then, the BEMS solves an optimization problem to maximize its own profit and determine the real-time TE market-clearing price. Afterward, based on the clearing price, the real-time scheduling of PEV batteries and the reimbursements to the PEV owners for their responses are determined. Additionally, the original mixed-integer non-linear optimization problem is reformulated as a mixed-integer linear programming one using a set of linearization techniques. Finally, the proposed model is applied to a residential building with 50 PEV charging piles, and the simulation results show that the proposed model decreases the actual charging payment of PEV owners by 17.6% and 52.3%, and the total cost of BEMS by 5.1% and 10.8% compared to demand response concept-based and uncontrolled charging models, respectively.

Three-Phase Unbalanced Distribution Network Dynamic Reconfiguration: A Distributionally Robust Approach

Abstract: The active distribution network has witnessed an increasing penetration of distributed generation (DG) while the stochasticity and variability arising from DGs also impose significant challenges on system operation. To mightily accommodate the uncertainty of DG, we introduce a distributionally robust chance-constrained dynamic reconfiguration approach for a three-phase unbalanced distribution network. The proposed framework optimizes the switching cost and the expected power supply cost from upstream grid, and stipulates that the chance constraints hold under the worst-case distribution within a novel ambiguity set, which incorporates the Wasserstein distance and the first-order moment. Then we develop tractable and scalable solution methods to tackle the expected objective function and chance constraints. As a result, the proposed model is reduced to a mixed-integer linear programming problem that can readily be implemented. Numerical experiments are carried out on the IEEE 34-bus and 123-bus test systems to demonstrate the effectiveness and efficiency of the suggested approach.

A column generation-based exact solution method for seru scheduling problems

Abstract: This paper attempts to address production scheduling problems in seru production systems (SPS), which is a new-type manufacturing system emanating from Japanese electronic assembly industry. As a typical parallel production system, SPS has high efficiency, good flexibility, and rapid responsiveness, which are achieved by reconfiguring serus, increasing, or decreasing workers to adjust the output in practical volatile markets. The seru scheduling problem in this paper is formulated as an integer programming (IP) model to minimize the total weighted completion time (TWCT). Then, by employing the Dantzig-Wolfe decomposition, the proposed IP model is reformulated into a set partitioning problem with a master problem and several subproblems. A branch-and-bound (B&B) algorithm is designed, and each node in a B&B tree is a linear relaxation problem (LRP) of the set partitioning problem. The LRP is solved by a column generation approach, in which each column is generated to represent a schedule of the seru in SPS based on solving the subproblems. Computational experiments are conducted, and the results indicate that the proposed column generation-based exact solution method is promising in solving the seru scheduling problem effectively.

Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings

Abstract: We consider the problem of computing a sequence of rankings that maximizes consumer-side utility while minimizing producer-side individual unfairness of exposure. While prior work has addressed this problem using linear or quadratic programs on bistochastic matrices, such approaches, relying on Birkhoff-von Neumann (BvN) decompositions, are too slow to be implemented at large scale. In this paper we introduce a geometrical object, a polytope that we call expohedron, whose points represent all achievable exposures of items for a Position Based Model (PBM). We exhibit some of its properties and lay out a Carathéodory decomposition algorithm with complexity $O(n^2łog(n))$ able to express any point inside the expohedron as a convex sum of at most n vertices, where n is the number of items to rank. Such a decomposition makes it possible to express any feasible target exposure as a distribution over at most n rankings. Furthermore we show that we can use this polytope to recover the whole Pareto frontier of the multi-objective fairness-utility optimization problem, using a simple geometrical procedure with complexity $O(n^2łog(n))$. Our approach compares favorably to linear or quadratic programming baselines in terms of algorithmic complexity and empirical runtime and is applicable to any merit that is a non-decreasing function of item relevance. Furthermore our solution can be expressed as a distribution over only $ doc$ permutations, instead of the $(n-1)^2 + 1$ achieved with BvN decompositions. We perform experiments on synthetic and real-world datasets, confirming our theoretical results.

Portfolio Insurance through Error-Correction Neural Networks

Abstract: Minimum-cost portfolio insurance (MCPI) is a well-known investment strategy that tries to limit the losses a portfolio may incur as stocks decrease in price without requiring the portfolio manager to sell those stocks. In this research, we define and study the time-varying MCPI problem as a time-varying linear programming problem. More precisely, using real-world datasets, three different error-correction neural networks are employed to address this financial TLPtime-varying linear programming problem in continuous-time. These neural network solvers are the zeroing NNneural network (ZNN), the linear-variational-inequality primal-dual NNneural network (LVI-PDNN), and the simplified LVI-PDNN (S-LVI-PDNN). The neural network solvers are tested using real-world data on portfolios of up to 20 stocks, and the results show that they are capable of solving the financial problem efficiently, in some cases more than five times faster than traditional methods, though their accuracy declines as the size of the portfolio increases. This demonstrates the speed and accuracy of neural network solvers, showing their superiority over traditional methods in moderate-size portfolios. To promote and contend the outcomes of this research, we created two MATLAB repositories for the interested user,research, we created two MATLAB repositories, for the interested user, that are publicly accessible on GitHub.

Image space branch-reduction-bound algorithm for globally minimizing a class of multiplicative problems

Abstract: This paper presents an image space branch-reduction-bound algorithm for solving a class of multiplicative problems (MP). First of all, by introducing auxiliary variables and taking the logarithm of the objective function, an equivalent problem (EP) of the problem (MP) is obtained. Next, by using a new linear relaxation technique, the parametric linear relaxation programming (PLRP) of the equivalence problem (EP) can be established for acquiring the lower bound of the optimal value to the problem (EP). Based on the characteristics of the objective function of the equivalent problem and the structure of the branch-and-bound algorithm, some region reduction techniques are constructed for improving the convergence speed of the algorithm. Finally, the global convergence of the algorithm is proved and its computational complexity is estimated, and numerical experiments are reported to indicate the higher computational performance of the algorithm.