scholarly journals Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Igor Litvinchev ◽  
Edith Lucero Ozuna Espinosa
Keyword(s):  
Large Scale ◽  
Optimization Problem ◽  
Continuous Optimization ◽  
Packing Problem ◽  
Regular Grid ◽  
Food Industries ◽  
Rectangular Container ◽  
Binary Problem ◽  
Weighted Number ◽  
Grid Nesting

A problem of packing a limited number of unequal circles in a fixed size rectangular container is considered. The aim is to maximize the (weighted) number of circles placed into the container or minimize the waste. This problem has numerous applications in logistics, including production and packing for the textile, apparel, naval, automobile, aerospace, and food industries. Frequently the problem is formulated as a nonconvex continuous optimization problem which is solved by heuristic techniques combined with local search procedures. New formulations are proposed for approximate solution of packing problem. The container is approximated by a regular grid and the nodes of the grid are considered as potential positions for assigning centers of the circles. The packing problem is then stated as a large scale linear 0-1 optimization problem. The binary variables represent the assignment of centers to the nodes of the grid. Nesting circles inside one another is also considered. The resulting binary problem is then solved by commercial software. Numerical results are presented to demonstrate the efficiency of the proposed approach and compared with known results.

A Metaheuristic Approach and Mathematical Programming for Packing Objects in a Rectangular Container

2020 ◽  
Vol 11 (3) ◽  
pp. 108-119
Author(s):  
Rafael Torres-Escobar ◽  
Jose Antonio Marmolejo-Saucedo ◽  
Igor Litvinchev
Keyword(s):  
Large Scale ◽  
Programming Model ◽  
Packing Problem ◽  
Population Based ◽  
Binary Decision ◽  
Rectangular Container ◽  
Decision Variables ◽  
Binary Problem ◽  
Python Programming ◽  
Set Of Points

The problem of packing non-congruent circles within bounded regions is considered. The aim is to maximize the number of circles placed into a rectangular container or minimize the waste. The circle is considered as a set of points that are all the same distance (not necessarily Euclidean) from a given point. An integer programming model is proposed using a dotted-board approximating the container and considering the dots as potential positions for assigning centers of the circles. The packing problem is then stated as a large scale linear 0–1 optimization problem. Binary decision variables are associated with each discrete point of the board (a dot) and with each object. Then, the same grid is used to prove a population-based metaheuristic. This metaheuristic is inspired by the monkeys' behavior. The resulting binary problem is then solved by using Gurobi Solver and Python Programming Language as Interface

scholarly journals Development and Characterization of Two Types of Surface Displayed Levansucrases for Levan Biosynthesis

Catalysts ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 757
Author(s):  
Huiyi Shang ◽  
Danni Yang ◽  
Dairong Qiao ◽  
Hui Xu ◽  
Yi Cao
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Molecular Weight ◽  
Large Scale ◽  
Surface Display ◽  
Yeast Surface Display ◽  
Fusion Partner ◽  
Whole Cell ◽  
Food Industries ◽  
Yeast Surface ◽  
The Stability

Levan has wide applications in chemical, cosmetic, pharmaceutical and food industries. The free levansucrase is usually used in the biosynthesis of levan, but the poor reusability and low stability of free levansucrase have limited its large-scale use. To address this problem, the surface-displayed levansucrase in Saccharomyces cerevisiae were generated and evaluated in this study. The levansucrase from Zymomonas mobilis was displayed on the cell surface of Saccharomyces cerevisiae EBY100 using a various yeast surface display platform. The N-terminal fusion partner is based on a-agglutinin, and the C-terminal one is Flo1p. The yield of levan produced by these two whole-cell biocatalysts reaches 26 g/L and 34 g/L in 24 h, respectively. Meanwhile, the stability of the surface-displayed levansucrases is significantly enhanced. After six reuses, these two biocatalysts retained over 50% and 60% of their initial activities, respectively. Furthermore, the molecular weight and polydispersity test of the products suggested that the whole-cell biocatalyst of levansucrase displayed by Flo1p has more potentials in the production of levan with low molecular weight which is critical in certain applications. In conclusion, our method not only enable the possibility to reuse the enzyme, but also improves the stability of the enzyme.

Dynamic output feedback control for nonlinear large-scale interconnected systems

2020 ◽  
Vol 39 (4) ◽  
pp. 801-821
Author(s):  
Ezzeddine Touti ◽  
Ali Sghaier Tlili ◽  
Muhannad Almutiry
Keyword(s):  
Decentralized Control ◽  
Output Feedback ◽  
Large Scale ◽  
Optimization Problem ◽  
Lyapunov Theory ◽  
Interconnected Systems ◽  
Dynamic Output Feedback ◽  
Content Type ◽  
Dynamic Output ◽  
Control Scheme

Purpose This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded. Design/methodology/approach Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs). Findings The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system. Originality/value The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

AN EFFICIENT APPROACH FOR THE THREE-DIMENSIONAL CONTAINER PACKING PROBLEM WITH PRACTICAL CONSTRAINTS

2004 ◽  
Vol 21 (03) ◽  
pp. 279-295 ◽  
Author(s):  
ZHIHONG JIN ◽  
KATSUHISA OHNO ◽  
JIALI DU
Keyword(s):  
Three Dimensional ◽  
Real Life ◽  
Packing Problem ◽  
Utilization Rate ◽  
Benchmark Problems ◽  
Rectangular Container ◽  
Efficient Packing ◽  
High Degree ◽  
Practical Constraints ◽  
Inherent Stability

This paper deals with the three-dimensional container packing problem (3DCPP), which is to pack a number of items orthogonally onto a rectangular container so that the utilization rate of the container space or the total value of loaded items is maximized. Besides the above objectives, some other practical constraints, such as loading stability, the rotation of items around the height axis, and the fixed loading (unloading) orders, must be considered for the real-life 3DCPP. In this paper, a sub-volume based simulated annealing meta-heuristic algorithm is proposed, which aims at generating flexible and efficient packing patterns and providing a high degree of inherent stability at the same time. Computational experiments on benchmark problems show its efficiency.

scholarly journals Nonlinear Steady-State Optimization of Large-Scale Gas Transmission Networks

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2832
Author(s):  
Andrzej J. Osiadacz ◽  
Małgorzata Kwestarz
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Optimization Problem ◽  
Operating Cost ◽  
Network Efficiency ◽  
Major Objective ◽  
Transmission Networks ◽  
Sqp Method ◽  
Gas Network ◽  
Compressor Power

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.

Proactive Optimization of Intelligent-Well Production Using Stochastic Gradient-Based Algorithms

2016 ◽  
Vol 19 (02) ◽  
pp. 239-252 ◽  
Author(s):  
Morteza Haghighat Sefat ◽  
Khafiz M. Muradov ◽  
Ahmed H. Elsheikh ◽  
David R. Davies
Keyword(s):  
Large Scale ◽  
Optimization Problem ◽  
Stochastic Gradient ◽  
Real Field ◽  
Directional Derivatives ◽  
Optimization Approach ◽  
Layer By Layer ◽  
Monitoring And Control ◽  
Ensemble Size ◽  
Local Optima

Summary The popularity of intelligent wells (I-wells), which provide layer-by-layer monitoring and control capability of production and injection, is growing. However, the number of available techniques for optimal control of I-wells is limited (Sarma et al. 2006; Alghareeb et al. 2009; Almeida et al. 2010; Grebenkin and Davies 2012). Currently, most of the I-wells that are equipped with interval control valves (ICVs) are operated to enhance the current production and to resolve problems associated with breakthrough of the unfavorable phase. This reactive strategy is unlikely to deliver the long-term optimum production. On the other side, the proactive-control strategy of I-wells, with its ambition to provide the optimum control for the entire well's production life, has the potential to maximize the cumulative oil production. This strategy, however, results in a high-dimensional, nonlinear, and constrained optimization problem. This study provides guidelines on selecting a suitable proactive optimization approach, by use of state-of-the-art stochastic gradient-approximation algorithms. A suitable optimization approach increases the practicality of proactive optimization for real field models under uncertain operational and subsurface conditions. We evaluate the simultaneous-perturbation stochastic approximation (SPSA) method (Spall 1992) and the ensemble-based optimization (EnOpt) method (Chen et al. 2009). In addition, we present a new derivation of the EnOpt by use of the concept of directional derivatives. The numerical results show that both SPSA and EnOpt methods can provide a fast solution to a large-scale and multiple I-well proactive optimization problem. A criterion for tuning the algorithms is proposed and the performance of both methods is compared for several test cases. The used methodology for estimating the gradient is shown to affect the application area of each algorithm. SPSA provides a rough estimate of the gradient and performs better in search environments, characterized by several local optima, especially with a large ensemble size. EnOpt was found to provide a smoother estimation of the gradient, resulting in a more-robust algorithm to the choice of the tuning parameters, and a better performance with a small ensemble size. Moreover, the final optimum operation obtained by EnOpt is smoother. Finally, the obtained criteria are used to perform proactive optimization of ICVs in a real field.

Spectral Efficiency Self-Optimization through Dynamic User Clustering and Beam Steering

2016 ◽  
pp. 137-155
Author(s):  
Md Salik Parwez ◽  
Hasan Farooq ◽  
Ali Imran ◽  
Hazem Refai
Keyword(s):  
Spectral Efficiency ◽  
Large Scale ◽  
Optimization Problem ◽  
Focal Point ◽  
Beam Steering ◽  
Clustering Algorithms ◽  
Performance Comparison ◽  
Base Stations ◽  
User Clustering ◽  
A Cell

This paper presents a novel scheme for spectral efficiency (SE) optimization through clustering of users. By clustering users with respect to their geographical concentration we propose a solution for dynamic steering of antenna beam, i.e., antenna azimuth and tilt optimization with respect to the most focal point in a cell that would maximize overall SE in the system. The proposed framework thus introduces the notion of elastic cells that can be potential component of 5G networks. The proposed scheme decomposes large-scale system-wide optimization problem into small-scale local sub-problems and thus provides a low complexity solution for dynamic system wide optimization. Every sub-problem involves clustering of users to determine focal point of the cell for given user distribution in time and space, and determining new values of azimuth and tilt that would optimize the overall system SE performance. To this end, we propose three user clustering algorithms to transform a given user distribution into the focal points that can be used in optimization; the first is based on received signal to interference ratio (SIR) at the user; the second is based on received signal level (RSL) at the user; the third and final one is based on relative distances of users from the base stations. We also formulate and solve an optimization problem to determine optimal radii of clusters. The performances of proposed algorithms are evaluated through system level simulations. Performance comparison against benchmark where no elastic cell deployed, shows that a gain in spectral efficiency of up to 25% is possible depending upon user distribution in a cell.

scholarly journals On the Sensitivity of Local Flexibility Markets to Forecast Error: A Bi-Level Optimization Approach

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1959
Author(s):  
Delaram Azari ◽  
Shahab Shariat Torbaghan ◽  
Hans Cappon ◽  
Karel J. Keesman ◽  
Madeleine Gibescu ◽  
...  
Keyword(s):  
Distribution System ◽  
Large Scale ◽  
Optimization Problem ◽  
Distribution Networks ◽  
Second Order ◽  
Optimization Approach ◽  
Second Order Cone ◽  
Local Flexibility ◽  
Level Problem ◽  
Relaxation Error

The large-scale integration of intermittent distributed energy resources has led to increased uncertainty in the planning and operation of distribution networks. The optimal flexibility dispatch is a recently introduced, power flow-based method that a distribution system operator can use to effectively determine the amount of flexibility it needs to procure from the controllable resources available on the demand side. However, the drawback of this method is that the optimal flexibility dispatch is inexact due to the relaxation error inherent in the second-order cone formulation. In this paper we propose a novel bi-level optimization problem, where the upper level problem seeks to minimize the relaxation error and the lower level solves the earlier introduced convex second-order cone optimal flexibility dispatch (SOC-OFD) problem. To make the problem tractable, we introduce an innovative reformulation to recast the bi-level problem as a non-linear, single level optimization problem which results in no loss of accuracy. We subsequently investigate the sensitivity of the optimal flexibility schedules and the locational flexibility prices with respect to uncertainty in load forecast and flexibility ranges of the demand response providers which are input parameters to the problem. The sensitivity analysis is performed based on the perturbed Karush–Kuhn–Tucker (KKT) conditions. We investigate the feasibility and scalability of the proposed method in three case studies of standardized 9-bus, 30-bus, and 300-bus test systems. Simulation results in terms of local flexibility prices are interpreted in economic terms and show the effectiveness of the proposed approach.

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