The Location Problem of Given and Indivisible Different Units

1970 ◽  
Vol 2 (3) ◽  
pp. 341-356
Author(s):  
G. Jándy
Keyword(s):  
Exact Solution ◽  
Heuristic Algorithm ◽  
Network Flow ◽  
Location Problem ◽  
Optimal Solution ◽  
Type Problem ◽  
Distribution Problem ◽  
Enumeration Algorithm ◽  
Weighted Distribution ◽  
Partial Enumeration

In cases where certain simplifications are allowed, the location optimisation of given and indivisible different economic units may be modelled as a bi-value weighted distribution problem. The paper presents a heuristic algorithm for this network-flow-type problem and also a partial enumeration algorithm for deriving the exact solution. But it is also pointed out that an initial sub-optimal solution can quickly be improved with a derivation on a direct line only, if the exact solution is not absolutely essential. A numerical example is used to illustrate the method of derivation on a direct line starting with an upper bound given by a sub-optimal solution.

scholarly journals Sensor Location Problem for Network Traffic Flow Derivation Based on Turning Ratios at Intersection

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Minhua Shao ◽  
Lijun Sun ◽  
Xianzhi Shao
Keyword(s):  
Network Flow ◽  
Location Problem ◽  
Optimal Solution ◽  
Coefficient Matrix ◽  
Sensor Location ◽  
The Road ◽  
Minimum Number ◽  
Flow Conservation ◽  
The Greedy Algorithm ◽  
Counting Points

The sensor location problem (SLP) discussed in this paper is to find the minimum number and optimum locations of the flow counting points in the road network so that the traffic flows over the whole network can be inferred uniquely. Flow conservation system at intersections is formulated firstly using the turning ratios as the prior information. Then the coefficient matrix of the flow conservation system is proved to be nonsingular. Based on that, the minimal number of counting points is determined to be the total number of exclusive incoming roads and dummy roads, which are added to the network to represent the trips generated on real roads. So the task of SLP model based on turning ratios is just to determine the optimal sensor locations. The following analysis in this paper shows that placing sensors on all the exclusive incoming roads and dummy roads can always generate a unique network flow vector for any network topology. After that, a detection set composed of only real roads is proven to exist from the view of feasibility in reality. Finally, considering the roads importance and cost of the sensors, a weighted SLP model is formulated to find the optimal detection set. The greedy algorithm is proven to be able to provide the optimal solution for the proposed weighted SLP model.

Application of the optimal network flow method to the problem of locomotive selection for freight trains on the Eastern Polygon

2019 ◽  
pp. 94-106
Author(s):  
Александр Борисович Шабунин ◽  
Андрей Куркенович Такмазьян
Keyword(s):  
Network Flow ◽  
Optimal Solution ◽  
Global Optimum ◽  
Full Scale ◽  
Scale Model ◽  
Test Cases ◽  
Processor Time ◽  
Flow Method ◽  
Optimal Network ◽  
Locomotive Assignment

Моделируется подбор тяговых ресурсов (локомотивов - в данном случае) для провоза грузовых поездов. В качестве входных данных рассматриваются маршрут поезда, время готовности поезда к отправлению, средняя скорость и вес поезда. Имеется множество локомотивов, обладающих грузоподъемностью и областью разрешенного действия. Цель - оптимально подобрать ресурс для каждого участка маршрута поезда. Решение ищется методом потока ресурсов минимальной суммарной стоимости через специально сконструированную сеть. Сеть построена на основе взвешенного орграфа из ребер графика поездов на линейных участках и ребер альтернативы, в процессе прохода по которым осуществляется “смена деятельности” локомотива (например, отцепление от одного поезда и подцепка к другому). Полученное решение обладает свойством глобальной оптимальности по времени. The selection of traction resources (locomotives) for the transport of freight trains is modelled. The input data are the train route, the readiness time of the train for departure, the average speed and weight of the train. In addition, there are many locomotives with a carrying capacity and an area of permitted action. The research objective is to optimally select a resource for each segment of the train route. The solution is sought by the resource flow method of the minimum total cost through a specially designed network. The network includes edges created from train schedule segments whose filling means locomotive assignment to train at the segment, and special alternative edges, passing through which a locomotive alternates its assignment. The algorithm for finding the optimal solution is the method of pushing through the pre-flow proposed by A. Goldberg and R. Tarjan. This is one of the fastest algorithms converging to a global optimum. Two test cases were investigated: a trivial one, out of six trains and three locomotives, and a more complicated one, which is a model example the size of 10% of the full scale model and consists of 150 trains. Full scale calculations provide planning of the freight transportation on the Eastern Operational domain of the Russian Railways. The model includes 1800 locomotives and about 3000 trains on the time horizon of 48 hours. Solution is found in less than 5 minutes of processor time for a PC powered by Intel(R) Pentium(R) G2010 2.80 GHz processor.

Multi-Objecitve Control of Dynamical Systems

1995 ◽  
Author(s):  
Petros Voulgaris
Keyword(s):  
Exact Solution ◽  
Duality Theory ◽  
Closed Loop ◽  
Finite Impulse Response ◽  
Optimal Solution ◽  
Standard Methods ◽  
Continuity Properties ◽  
Step Procedure ◽  
Quadratic Programming Problems ◽  
Finite Step

Abstract In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.

Heuristic algorithm for optimal redundancy allocation in complex systems

2019 ◽  
Vol 25 (1) ◽  
pp. 54-64 ◽  
Author(s):  
Sudhanshu Aggarwal
Keyword(s):  
Complex Systems ◽  
Heuristic Algorithm ◽  
Communication Systems ◽  
Heuristic Algorithms ◽  
Real Life ◽  
Optimal Solution ◽  
Systems Design ◽  
Computational Time ◽  
Coherent System ◽  
Content Type

PurposeThe purpose of this paper is to present an efficient heuristic algorithm based on the 3-neighborhood approach. In this paper, search is made from sides of both feasible and infeasible regions to find near-optimal solutions.Design/methodology/approachThe algorithm performs a series of selection and exchange operations in 3-neighborhood to see whether this exchange yields still an improved feasible solution or converges to a near-optimal solution in which case the algorithm stops.FindingsThe proposed algorithm has been tested on complex system structures which have been widely used. The results show that this 3-neighborhood approach not only can obtain various known solutions but also is computationally efficient for various complex systems.Research limitations/implicationsIn general, the proposed heuristic is applicable to any coherent system with no restrictions on constraint functions; however, to enforce convergence, inferior solutions might be included only when they are not being too far from the optimum.Practical implicationsIt is observed that the proposed heuristic is reasonably proficient in terms of various measures of performance and computational time.Social implicationsReliability optimization is very important in real life systems such as computer and communication systems, telecommunications, automobile, nuclear, defense systems, etc. It is an important issue prior to real life systems design.Originality/valueThe utilization of 3-neighborhood strategy seems to be encouraging as it efficiently enforces the convergence to a near-optimal solution; indeed, it attains quality solutions in less computational time in comparison to other existing heuristic algorithms.

scholarly journals Robust Satellite Scheduling Approach for Dynamic Emergency Tasks

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Xuejun Zhai ◽  
Xiaonan Niu ◽  
Hong Tang ◽  
Lixin Wu ◽  
Yonglin Shen
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithm ◽  
Optimal Solution ◽  
Simulation Experiments ◽  
Multiobjective Genetic Algorithm ◽  
Scheduling Model ◽  
Rapid Responses ◽  
Earth Observation Satellites ◽  
Satellite Scheduling ◽  
Combined Algorithm

Earth observation satellites play a significant role in rapid responses to emergent events on the Earth’s surface, for example, earthquakes. In this paper, we propose a robust satellite scheduling model to address a sequence of emergency tasks, in which both the profit and robustness of the schedule are simultaneously maximized in each stage. Both the multiobjective genetic algorithm NSGA2 and rule-based heuristic algorithm are employed to obtain solutions of the model. NSGA2 is used to obtain a flexible and highly robust initial schedule. When every set of emergency tasks arrives, a combined algorithm called HA-NSGA2 is used to adjust the initial schedule. The heuristic algorithm (HA) is designed to insert these tasks dynamically to the waiting queue of the initial schedule. Then the multiobjective genetic algorithm NSGA2 is employed to find the optimal solution that has maximum revenue and robustness. Meanwhile, to improve the revenue and resource utilization, we adopt a compact task merging strategy considering the duration of task execution in the heuristic algorithm. Several experiments are used to evaluate the performance of HA-NSGA2. All simulation experiments show that the performance of HA-NSGA2 is significantly improved.

scholarly journals An ADD/DROP procedure for the capacitated plant location problem

2004 ◽  
Vol 24 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Claudio Thomas Bornstein ◽  
Manoel Campêlo
Keyword(s):  
Heuristic Algorithm ◽  
Location Problem ◽  
Lagrangean Relaxation ◽  
Upper Bounds ◽  
Transportation Costs ◽  
Plant Location ◽  
Computational Results ◽  
Lower And Upper Bounds

The capacitated plant location problem with linear transportation costs is considered. Exact rules and heuristics are presented for opening or closing of facilities. A heuristic algorithm based on ADD/DROP strategies is proposed. Procedures are implemented with the help of lower and upper bounds using Lagrangean relaxation. Computational results are presented and comparisons with other algorithms are made.

Direct Gravitational Search Algorithm for Global Optimisation Problems

2016 ◽  
Vol 6 (3) ◽  
pp. 290-313 ◽  
Author(s):  
Ahmed F. Ali ◽  
Mohamed A. Tawhid
Keyword(s):  
Heuristic Algorithm ◽  
Hybrid Algorithm ◽  
Search Algorithm ◽  
Direct Method ◽  
Gravitational Search Algorithm ◽  
Optimal Solution ◽  
Slow Convergence ◽  
Gravitational Search ◽  
Law Of Gravity ◽  
Number Of Iterations

AbstractA gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms, and the numerical results show the optimal or near optimal solution is obtained faster.

Initial attempt to optimize the operation of a hydrometric network using branch and bound algorithm

1988 ◽  
Vol 15 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Patrice M. Pelletier ◽  
Slobodan P. Simonovic
Keyword(s):  
Heuristic Algorithm ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Traveling Salesman ◽  
Future Research ◽  
Initial Attempt ◽  
Research Directions ◽  
New Approach ◽  
Future Research Directions ◽  
Field Area

The paper presents a new approach developed to formulate and solve the problem of field operation of a hydrometric network. In present practice, optimization techniques are not used for solving this problem. In the initial attempt, documented in the paper, the traveling salesman algorithm is used to find the optimal solution. Assumptions used and experience gained during the research are addressed in the paper. For the Dauphin hydrometric field area in Manitoba, an "optimal" solution has been obtained and presented. Based on the analysis of the results, conclusions were drawn about future research directions incorporating development of an effective heuristic algorithm for solving the traveling hydrometric technician problem. Key words: operation, hydrometric network, optimization, heuristic algorithm, traveling salesman algorithm.

Cross Warehouse Scheduling of Logistics Distribution and Cycle Re-Claimer Based on Heuristics Algorithm

2014 ◽  
Vol 644-650 ◽  
pp. 2606-2610 ◽  
Author(s):  
Rong Hua Ma
Keyword(s):  
Heuristic Algorithm ◽  
Programming Model ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Simulation Method ◽  
New Method ◽  
Logistics Distribution ◽  
Suboptimal Solution ◽  
Taboo Search Algorithm ◽  
Heuristics Algorithm

In the uncertain environment, the cycle re-claimer and logistics distribution cross warehouse scheduling is important and it should be optimized. The mathematical programming model is constructed, and the proposed two-stage heuristic algorithm is proposed, the optimal solution of heuristic algorithm is used as the initial value. And the taboo search algorithm is designed to improve the initial solution. In order to verify the availability of the method, the Monte Carlo simulation method is used for numerical experiment. The experiment results show that the new method can solve the suboptimal solution which close to the optimal solution in fast, and the taboo searching algorithm can improve the solution of heuristic algorithm, it has significantly improvement performance for new method, and it has good application value in practice.

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