scholarly journals The Color Mix Problem

2021 ◽  
Vol 11 (16) ◽  
pp. 7263
Author(s):  
Alfonsas Misevičius ◽  
Aleksandras Andrejevas ◽  
Armantas Ostreika ◽  
Tomas Blažauskas ◽  
Liudas Motiejūnas
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Quadratic Assignment Problem ◽  
Combinatorial Optimization Problem ◽  
Quadratic Assignment ◽  
Tabu Search Algorithm ◽  
Excellent Performance ◽  
Grey Pattern ◽  
Iterated Tabu Search

In this paper, we introduce a new combinatorial optimization problem entitled the color mix problem (CMP), which is a more general case of the grey pattern quadratic assignment problem (GP-QAP). Also, we propose an original hybrid genetic-iterated tabu search algorithm for heuristically solving the CMP. In addition, we present both analytical solutions and graphical visualizations of the obtained solutions, which clearly demonstrate the excellent performance of the proposed heuristic algorithm.

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.

scholarly journals A 2-Level Iterated Tabu Search Algorithm for the Quadratic Assignment Problem

2020 ◽  
Vol 90 ◽  
pp. 96-115
Author(s):  
Alfonsas Misevičius ◽  
Dovilė Kuznecovaitė (Verenė)
Keyword(s):  
Tabu Search ◽  
Assignment Problem ◽  
Search Algorithm ◽  
Quadratic Assignment Problem ◽  
Test Sample ◽  
Quadratic Assignment ◽  
Search Process ◽  
Tabu Search Algorithm ◽  
Overall Performance ◽  
Iterated Tabu Search

In this paper, a 2-level iterated tabu search (ITS) algorithm for the solution of the quadratic assignment problem (QAP) is considered. The novelty of the proposed ITS algorithm is that the solution mutation procedures are incorporated within the algorithm, which enable to diversify the search process and eliminate the search stagnation, thus increasing the algorithm’s efficiency. In the computational experiments, the algorithm is examined with various implemented variants of the mutation procedures using the QAP test (sample) instances from the library of the QAP instances – QAPLIB. The results of these experiments demonstrate how the different mutation procedures affect and possibly improve the overall performance of the ITS algorithm.

scholarly journals A 2-Level Iterated Tabu Search Algorithm for the Quadratic Assignment Problem

2019 ◽  
Vol 85 ◽  
pp. 115-134
Author(s):  
Alfonsas Misevičius ◽  
Dovilė Kuznecovaitė (Verenė)
Keyword(s):  
Tabu Search ◽  
Assignment Problem ◽  
Search Algorithm ◽  
Quadratic Assignment Problem ◽  
Test Sample ◽  
Quadratic Assignment ◽  
Search Process ◽  
Tabu Search Algorithm ◽  
Overall Performance ◽  
Iterated Tabu Search

 In this paper, a 2-level iterated tabu search (ITS) algorithm for the solution of the quadratic assignment problem (QAP) is considered. The novelty of the proposed ITS algorithm is that the solution mutation procedures are incorporated within the algorithm, which enable to diversify the search process and eliminate the search stagnation, thus increasing the algorithm’s efficiency. In the computational experiments, the algorithm is examined with various implemented variants of the mutation procedures using the QAP test (sample) instances from the library of the QAP instances – QAPLIB. The results of these experiments demonstrate how the different mutation procedures affect and possibly improve the overall performance of the ITS algorithm.

scholarly journals ITERATED TABU SEARCH: AN IMPROVEMENT TO STANDARD TABU SEARCH

2006 ◽  
Vol 35 (3) ◽  
Author(s):  
Alfonsas Misevicius ◽  
Antanas Lenkevicius ◽  
Dalius Rubliauskas
Keyword(s):  
Combinatorial Optimization ◽  
Tabu Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Special Kind ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Diversification Mechanism ◽  
Iterated Tabu Search

The goal of this paper is to discuss the tabu search (TS) meta-heuristic and its enhancement for combinatorial optimization problems. Firstly, the issues related to the principles and specific features of the standard TS are concerned. Further, a promising extension to the classical tabu search scheme is introduced. The most important component of this extension is a special kind of diversification mechanism. We give the paradigm of this new improved TS strategy, which is called an iterated tabu search (ITS). ITS was applied to the difficult combinatorial optimization problems, the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). The results of the experiments with the TSP and QAP show the high efficiency of the ITS strategy. The outstanding performance of ITS is also demonstrated by the fact that the new record-breaking solutions were found for the hard QAP instances - tai80a and tai100a.

scholarly journals From Decimation to Local Search and Back: A New Approach to MaxSAT

2017 ◽  
Author(s):  
Shaowei Cai ◽  
Chuan Luo ◽  
Haochen Zhang
Keyword(s):  
Combinatorial Optimization ◽  
Local Search ◽  
Optimization Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Combinatorial Optimization Problem ◽  
Np Hard ◽  
Local Search Algorithm ◽  
Maximum Satisfiability ◽  
New Approach

Maximum Satisfiability (MaxSAT) is an important NP-hard combinatorial optimization problem with many applications and MaxSAT solving has attracted much interest. This work proposes a new incomplete approach to MaxSAT. We propose a novel decimation algorithm for MaxSAT, and then combine it with a local search algorithm. Our approach works by interleaving between the decimation algorithm and the local search algorithm, with useful information passed between them. Experiments show that our solver DeciLS achieves state of the art performance on all unweighted benchmarks from the MaxSAT Evaluation 2016. Moreover, compared to SAT-based MaxSAT solvers which dominate industrial benchmarks for years, it performs better on industrial benchmarks and significantly better on application formulas from SAT Competition. We also extend this approach to (Weighted) Partial MaxSAT, and the resulting solvers significantly improve local search solvers on crafted and industrial benchmarks, and are complementary (better on WPMS crafted benchmarks) to SAT-based solvers.

scholarly journals Enriching Documents with Compact, Representative, Relevant Knowledge Graphs

2020 ◽  
Author(s):  
Shuxin Li ◽  
Zixian Huang ◽  
Gong Cheng ◽  
Evgeny Kharlamov ◽  
Kalpa Gunaratna
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Combinatorial Optimization Problem ◽  
User Studies ◽  
Knowledge Graph ◽  
Trade Off ◽  
Best First Search ◽  
Knowledge Graphs

A prominent application of knowledge graph (KG) is document enrichment. Existing methods identify mentions of entities in a background KG and enrich documents with entity types and direct relations. We compute an entity relation subgraph (ERG) that can more expressively represent indirect relations among a set of mentioned entities. To find compact, representative, and relevant ERGs for effective enrichment, we propose an efficient best-first search algorithm to solve a new combinatorial optimization problem that achieves a trade-off between representativeness and compactness, and then we exploit ontological knowledge to rank ERGs by entity-based document-KG and intra-KG relevance. Extensive experiments and user studies show the promising performance of our approach.

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