scholarly journals Lower and upper bounds for the continuous single facility location problem in the presence of a forbidden region and travel barrier

2020 ◽  
Author(s):  
Intesar Al-Mudahka ◽  
Marwa S. Al-Jeraiwi ◽  
Rym M’Hallah
Keyword(s):  
Objective Function ◽  
Upper Bound ◽  
Location Problem ◽  
Search Space ◽  
Upper Bounds ◽  
Divide And Conquer ◽  
Mixed Integer ◽  
Quadratic Constraints ◽  
Forbidden Region ◽  
Single Facility

In this paper, we investigate FRB, which is the single facility Euclidean location problem in the presence of a (non-)convex polygonal forbidden region where travel and location are not permitted. We search for a new facility’s location that minimizes the weighted Euclidean distances to existing ones. To overcome the non-convexity and non-differentiability of the problem’s objective function, we propose an equivalent reformulation (RFRB) whose objective is linear. Using RFRB, we limit the search space to regions of a set of non-overlapping candidate domains that may contain the optimum; thus we reduce RFRB to a finite series of tight mixed integer convex programming sub-problems. Each sub-problem has a linear objective function and both linear and quadratic constraints that are defined on a candidate domain. Based on these sub-problems, we propose an efficient bounding-based algorithm (BA) that converges to a (near-)optimum. Within BA, we use two lower and four upper bounds for the solution value of FRB. The two lower and two upper bounds are solution values of relaxations of the restricted problem. The third upper bound is the near-optimum of a nested partitioning heuristic. The fourth upper bound is the outcome of a divide and conquer technique that solves a smooth sub-problem for each sub-region. We reveal via our computational investigation that BA matches an existing upper bound and improves two more.

scholarly journals Lookahead-Based SMT Solving

10.29007/gzzf ◽  
2018 ◽  
Author(s):  
Antti Hyvärinen ◽  
Matteo Marescotti ◽  
Parvin Sadigova ◽  
Hana Chockler ◽  
Natasha Sharygina
Keyword(s):  
Upper Bound ◽  
Binary Tree ◽  
Search Space ◽  
Divide And Conquer ◽  
Constraint Solving ◽  
Prototype Implementation ◽  
Smt Solver ◽  
Smt Solving ◽  
Clause Learning

The lookahead approach for binary-tree-based search in constraint solving favors branching that provide the lowest upper bound for the remaining search space. The approach has recently been applied in instance partitioning in divide-and-conquer-based parallelization, but in general its connection to modern, clause-learning solvers is poorly understood. We show two ways of combining lookahead approach with a modern DPLL(T)-based SMT solver fully profiting from theory propagation, clause learning, and restarts. Our thoroughly tested prototype implementation is surprisingly efficient as an independent SMT solver on certain instances, in particular when applied to a non-convex theory, where the lookahead-based implementation solves 40% more unsatisfiable instances compared to the standard implementation.

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

scholarly journals On-Shelf Utility Mining of Sequence Data

2021 ◽  
Vol 16 (2) ◽  
pp. 1-31
Author(s):  
Chunkai Zhang ◽  
Zilin Du ◽  
Yuting Yang ◽  
Wensheng Gan ◽  
Philip S. Yu
Keyword(s):  
High Efficiency ◽  
Sequence Data ◽  
Real Life ◽  
Search Space ◽  
Upper Bounds ◽  
Utility Mining ◽  
Limited Memory ◽  
Time Periods ◽  
High Utility ◽  
Synthetic Datasets

Utility mining has emerged as an important and interesting topic owing to its wide application and considerable popularity. However, conventional utility mining methods have a bias toward items that have longer on-shelf time as they have a greater chance to generate a high utility. To eliminate the bias, the problem of on-shelf utility mining (OSUM) is introduced. In this article, we focus on the task of OSUM of sequence data, where the sequential database is divided into several partitions according to time periods and items are associated with utilities and several on-shelf time periods. To address the problem, we propose two methods, OSUM of sequence data (OSUMS) and OSUMS + , to extract on-shelf high-utility sequential patterns. For further efficiency, we also design several strategies to reduce the search space and avoid redundant calculation with two upper bounds time prefix extension utility ( TPEU ) and time reduced sequence utility ( TRSU ). In addition, two novel data structures are developed for facilitating the calculation of upper bounds and utilities. Substantial experimental results on certain real and synthetic datasets show that the two methods outperform the state-of-the-art algorithm. In conclusion, OSUMS may consume a large amount of memory and is unsuitable for cases with limited memory, while OSUMS + has wider real-life applications owing to its high efficiency.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

scholarly journals Location of regional and international hub ports in liner shipping

2017 ◽  
Vol 2 (2) ◽  
pp. 114-125 ◽  
Author(s):  
Jianfeng Zheng ◽  
Cong Fu ◽  
Haibo Kuang
Keyword(s):  
Design Methodology ◽  
Location Problem ◽  
Programming Model ◽  
Liner Shipping ◽  
Mixed Integer ◽  
Eastern Asia ◽  
Hub Location ◽  
Hub Location Problem ◽  
Content Type ◽  
Western Asia

Purpose This paper aims to investigate the location of regional and international hub ports in liner shipping by proposing a hierarchical hub location problem. Design/methodology/approach This paper develops a mixed-integer linear programming model for the authors’ proposed problem. Numerical experiments based on a realistic Asia-Europe-Oceania liner shipping network are carried out to account for the effectiveness of this model. Findings The results show that one international hub port (i.e. Rotterdam) and one regional hub port (i.e. Zeebrugge) are opened in Europe. Two international hub ports (i.e. Sokhna and Salalah) are located in Western Asia, where no regional hub port is established. One international hub port (i.e. Colombo) and one regional hub port (i.e. Cochin) are opened in Southern Asia. One international hub port (i.e. Singapore) and one regional hub port (i.e. Jakarta) are opened in Southeastern Asia and Australia. Three international hub ports (i.e. Hong Kong, Shanghai and Yokohama) and two regional hub ports (i.e. Qingdao and Kwangyang) are opened in Eastern Asia. Originality/value This paper proposes a hierarchical hub location problem, in which the authors distinguish between regional and international hub ports in liner shipping. Moreover, scale economies in ship size are considered. Furthermore, the proposed problem introduces the main ports.

Nonlinear Optimal Design of Dynamic Mechanical Systems

1992 ◽  
Author(s):  
T. E. Potter ◽  
K. D. Willmert ◽  
M. Sathyamoorthy
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Iteration Process ◽  
Optimization Method ◽  
Linear Constraints ◽  
Sum Of Squares ◽  
Function Evaluation ◽  
Deformation Analysis ◽  
Nonlinear Constraints ◽  
Quadratic Constraints

Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

scholarly journals Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-27 ◽  
Author(s):  
Claudio Araya-Sassi ◽  
Pablo A. Miranda ◽  
Germán Paredes-Belmar
Keyword(s):  
Inventory Control ◽  
Lagrangian Relaxation ◽  
Location Problem ◽  
Subgradient Method ◽  
Capacity Constraints ◽  
Mixed Integer ◽  
Total System ◽  
Periodic Review ◽  
Decomposition Approach ◽  
Stochastic Capacity

We studied a joint inventory location problem assuming a periodic review for inventory control. A single plant supplies a set of products to multiple warehouses and they serve a set of customers or retailers. The problem consists in determining which potential warehouses should be opened and which retailers should be served by the selected warehouses as well as their reorder points and order sizes while minimizing the total costs. The problem is a Mixed Integer Nonlinear Programming (MINLP) model, which is nonconvex in terms of stochastic capacity constraints and the objective function. We propose a solution approach based on a Lagrangian relaxation and the subgradient method. The decomposition approach considers the relaxation of different sets of constraints, including customer assignment, warehouse demand, and variance constraints. In addition, we develop a Lagrangian heuristic to determine a feasible solution at each iteration of the subgradient method. The proposed Lagrangian relaxation algorithm provides low duality gaps and near-optimal solutions with competitive computational times. It also shows significant impacts of the selected inventory control policy into total system costs and network configuration, when it is compared with different review period values.

scholarly journals Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Chu ◽  
Lu Wang ◽  
Xin Liu ◽  
Chengbin Chu ◽  
Yang Sui
Keyword(s):  
Probability Distribution ◽  
Location Problem ◽  
Service Level ◽  
Mixed Integer ◽  
Distribution Free ◽  
Demand Information ◽  
The Mean ◽  
Constrained Model ◽  
Short Time ◽  
Ambulance Location

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

Upper bounds on the energy dissipation in turbulent precession

1996 ◽  
Vol 321 ◽  
pp. 335-370 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Viscous Dissipation ◽  
Upper Bound ◽  
Dissipation Rate ◽  
Oblate Spheroid ◽  
Upper Bounds ◽  
Precession Rate ◽  
Long Cylinder

Rigorous upper bounds on the viscous dissipation rate are identified for two commonly studied precessing fluid-filled configurations: an oblate spheroid and a long cylinder. The latter represents an interesting new application of the upper-bounding techniques developed by Howard and Busse. A novel ‘background’ method recently introduced by Doering & Constantin is also used to deduce in both instances an upper bound which is independent of the fluid's viscosity and the forcing precession rate. Experimental data provide some evidence that the observed viscous dissipation rate mirrors this behaviour at sufficiently high precessional forcing. Implications are then discussed for the Earth's precessional response.

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