scholarly journals Estimates of objective function minimum for solving linear fractional unconstrained combinatorial optimization problems on arrangements

2021 ◽  
pp. 32-36
Author(s):  
Tetiana Barbolina
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Numerical Experiments ◽  
Polynomial Algorithm ◽  
Optimization Problems ◽  
Finite Sequence ◽  
Feasible Set ◽  
Combinatorial Optimization Problems ◽  
Unconstrained Problems

The paper is devoted to the study of one class of Euclidean combinatorial optimization problems — combinatorial optimization problems on the general set of arrangements with linear fractional objective function and without additional (non-combinatorial) constraints. The paper substantiates the improvement of the polynomial algorithm for solving the specified class of problems. This algorithm foresees solving a finite sequence of linear unconstrained problems of combinatorial optimization on arrangements. The modification of the algorithm is based on the use of estimates of the objective function on the feasible set. This allows to exclude some of the problems from consideration and reduce the number of problems to be solved. The numerical experiments confirm the practical efficiency of the proposed approach.

scholarly journals A Methodology to Find the Elementary Landscape Decomposition of Combinatorial Optimization Problems

2011 ◽  
Vol 19 (4) ◽  
pp. 597-637 ◽  
Author(s):  
Francisco Chicano ◽  
L. Darrell Whitley ◽  
Enrique Alba
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Combinatorial Optimization Problem ◽  
Quadratic Assignment ◽  
Neighborhood Structure ◽  
Combinatorial Optimization Problems ◽  
Elementary Landscape

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.

Research on MPI-Based Parallel Max-Min Ant System

2012 ◽  
Vol 198-199 ◽  
pp. 1321-1326 ◽  
Author(s):  
Yu Liu ◽  
Guo Dong Wu
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

scholarly journals Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems

2020 ◽  
Vol 34 (02) ◽  
pp. 1603-1610 ◽  
Author(s):  
Jayanta Mandi ◽  
Emir Demirovi? ◽  
Peter J. Stuckey ◽  
Tias Guns
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Machine Learning Techniques ◽  
Scheduling Problems ◽  
Combinatorial Optimization Problems ◽  
Main Challenge ◽  
Linear Programming Problems

Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function, are fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estimation. Recently, Smart Predict and Optimize (SPO) has been proposed for problems with a linear objective function over the predictions, more specifically linear programming problems. It takes the regret of the predictions on the linear problem into account, by repeatedly solving it during learning. We investigate the use of SPO to solve more realistic discrete optimization problems. The main challenge is the repeated solving of the optimization problem. To this end, we investigate ways to relax the problem as well as warm-starting the learning and the solving. Our results show that even for discrete problems it often suffices to train by solving the relaxation in the SPO loss. Furthermore, this approach outperforms the state-of-the-art approach of Wilder, Dilkina, and Tambe. We experiment with weighted knapsack problems as well as complex scheduling problems, and show for the first time that a predict-and-optimize approach can successfully be used on large-scale combinatorial optimization problems.

Cellular Competitive Decision Algorithm for Minimum Ratio Spanning Tree

2012 ◽  
Vol 490-495 ◽  
pp. 365-369 ◽  
Author(s):  
Xiao Hua Xiong ◽  
Ai Bing Ning
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Heuristic Algorithm ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Optimization Problems ◽  
Decision Algorithm ◽  
Combinatorial Optimization Problems ◽  
Linear Cost ◽  
Minimum Ratio

Minimum ratio spanning tree(MRST) is the problem of finding a minimum spanning tree when the objective function is the ratio of two linear cost functions(such as the ratio of cost to weight). MRST problem is NP-hard when the denominator is unrestricted in sign. Cellular Competitive decision algorithm(CCDA) is a newly proposed meta-heuristic algorithm for solving combinatorial optimization problems. In this paper, a cellular competitive decision algorithm for MRST is presented. To verify the efficiency of the algorithm, it is been coded in Delphi 7, by which series of instances are tested and results result in good performance.

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