Solving the conditional optimization problem for a fractional linear objective function on a set of arrangements by the branch and bound method

2012 ◽  
Vol 48 (6) ◽  
pp. 832-836 ◽  
Author(s):  
I. V. Sergienko ◽  
O. A. Iemets ◽  
O. A. Chernenko
Keyword(s):  
Objective Function ◽  
Branch And Bound ◽  
Optimization Problem ◽  
Branch And Bound Method ◽  
Linear Objective Function ◽  
Conditional Optimization

ON COMPUTATIONAL COMPLEXITY OF HIERARCHICAL OPTIMIZATION

2002 ◽  
Vol 13 (05) ◽  
pp. 667-670
Author(s):  
WEIJIA JIA ◽  
ZHIBIN SUN
Keyword(s):  
Nash Equilibrium ◽  
Computational Complexity ◽  
Objective Function ◽  
Optimization Problem ◽  
Linear Constraints ◽  
The Other ◽  
Hierarchical Optimization ◽  
Linear Objective Function ◽  
Decision Variables

In this work, the computational complexity of a hierarchic optimization problem involving in several players is studied. Each player is assigned with a linear objective function. The set of variables is partitioned such that each subset corresponds to one player as its decision variables. All the players jointly make a decision on the values of these variables such that a set of linear constraints should be satisfied. One special player, called the leader, makes decision on its decision variables before of all the other players. The rest, after learnt of the decision of the leader, make their choices so that their decisions form a Nash Equilibrium for them, breaking tie by maximizing the objective function of player. We show that the exact complexity of the problem is FPNP-complete.

scholarly journals Optimisasi Program Linear Integer Murni Dengan Metode Branch And Bound

2018 ◽  
Vol 1 (2) ◽  
pp. 175-181
Author(s):  
Tondi Marulizar ◽  
Ujian Sinulingga ◽  
Esther Nababan
Keyword(s):  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Simplex Method ◽  
Optimization Problem ◽  
Linear Program ◽  
Integer Linear Program ◽  
Branch And Bound Method ◽  
A Value ◽  
Calculation Process ◽  
Lower Limits

Program Linier Integer Murni merupakan optimisasi kombinatorial yang tidak mudah untuk diselesaikan secara efisien. Metode yang sering digunakan untuk menyelesaikan Program Linier Integer Murni diantaranya adalah metode merative, yang merupakan salah satunya metode Branch and Bound. Metode ini menggunakan hasil dari metode simpleks yang belum bernilai integer sehingga dilakukan pencabangan dan batasan terhadap variabel x_j yang bernilai pecahan terbesar. Metode Branch and Bound dapat menyelesaikan masalah optimisasi suatu produk, tetapi membutuhkan waktu yang lebih lama dalam proses perhitungannya dikarenakan dalam setiap tahap perhitungan harus dicari nilai dari batas atas dan batas bawah yang ditentuan berdasarkan suatubatasandankriteria tertentu. Pure Integer Linear Program is combinatorial optimization that is not easy to solve efficiently. The method that is often used to complete the Pure Integer Linear Program is the merative method, which is one of the Branch and Bound methods. This method uses the results of the simplex method that is not yet an integer value so that the branching and limitation of the x_j variable is the largest fraction. The Branch and Bound method can solve the optimization problem of a product, but requires a longer time in the calculation process because in each calculation phase, a value must be sought from the upper and lower limits determined based on the boundary and certain criteria. 

scholarly journals Finding the Optimal Solution to the Problem of Conditional Optimization on the Graph of the set of Placements

2020 ◽  
pp. 29-34
Author(s):  
L.M. Koliechkina ◽  
◽  
A.M. Nahirna ◽  
Keyword(s):  
Euclidean Space ◽  
Objective Function ◽  
Linear Form ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Search Path ◽  
Conditional Optimization

The model of the problem of conditional optimization on the set of partial permutations is formulated. The linear form of the objective function is obtained by interpreting the elements of the set of partial permutations as points of the Euclidean space. A combinatorial polytope of allocations is considered for which there is a graph of the set of partial permutations An algorithm for solving this problem is proposed and its practical applicability is demonstrated. The proposed algorithm for solving the conditional optimization problem provides for the representation of the admissible of the Set of Partial Permutations in the form of a graph, which significantly reduces the search path for the optimal solution, as evidenced by the practical example considered.

scholarly journals Hypergraph Optimization Problems: Why is the Objective Function Linear?

1996 ◽  
Vol 3 (50) ◽  
Author(s):  
Aleksandar Pekec
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
A Priori ◽  
Point Of View ◽  
Linear Objective Function ◽  
Discrete Structures

Choosing an objective function for an optimization problem is a<br />modeling issue and there is no a-priori reason that the objective function<br />must be linear. Still, it seems that linear 0-1 programming formulations<br />are overwhelmingly used as models for optimization problems<br />over discrete structures. We show that this is not an accident. Under<br />some reasonable conditions (from the modeling point of view), the<br />linear objective function is the only possible one.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

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