scholarly journals Application of CMSA to the Minimum Positive Influence Dominating Set Problem

2021 ◽  
Author(s):  
Mehmet Anıl Akbay ◽  
Christian Blum
Keyword(s):  
Optimization Problems ◽  
Dominating Set ◽  
Positive Influence ◽  
Problem Instance ◽  
Medium Size ◽  
Combinatorial Optimization Problems ◽  
The Family ◽  
Np Hard Problem ◽  
Dominating Set Problem ◽  
Problem Instances

Construct, Merge, Solve & Adapt (CMSA) is a recently developed algorithm for solving combinatorial optimization problems. It combines heuristic elements, such as the probabilistic generation of solutions, with an exact solver that is iteratively applied to sub-instances of the tackled problem instance. In this paper, we present the application of CMSA to an NP-hard problem from the family of dominating set problems in undirected graphs. More specifically, the application in this paper concerns the minimum positive influence dominating set problem, which has applications in social networks. The obtained results show that CMSA outperforms the current state-of-the-art metaheuristics from the literature. Moreover, when instances of small and medium size are concerned CMSA finds many of the optimal solutions provided by CPLEX, while it clearly outperforms CPLEX in the context of the four largest, respectively more complicated, problem instances.

scholarly journals Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 361
Author(s):  
Teddy Nurcahyadi ◽  
Christian Blum
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Optimization Problems ◽  
Dominating Set ◽  
Ant Colony ◽  
Alternative Mechanism ◽  
Learning Approaches ◽  
Learning Mechanisms ◽  
Combinatorial Optimization Problems ◽  
Dominating Set Problem

Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based metaheuristics such as evolutionary algorithms and particle swarm optimization. Examples from nature, however, indicate that negative learning—in addition to positive learning—can beneficially be used for certain purposes. Several research papers have explored this topic over the last decades in the context of ant colony optimization, mostly with limited success. In this work we present and study an alternative mechanism making use of mathematical programming for the incorporation of negative learning in ant colony optimization. Moreover, we compare our proposal to some well-known existing negative learning approaches from the related literature. Our study considers two classical combinatorial optimization problems: the minimum dominating set problem and the multi dimensional knapsack problem. In both cases we are able to show that our approach significantly improves over standard ant colony optimization and over the competing negative learning mechanisms from the literature.

scholarly journals A QUBO Formulation of Minimum Multicut Problem Instances in Trees for D-Wave Quantum Annealers

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
William Cruz-Santos ◽  
Salvador E. Venegas-Andraca ◽  
Marco Lanzagorta
Keyword(s):  
Optimization Problems ◽  
Theoretical Computer Science ◽  
Scaling Analysis ◽  
Quantum Annealing ◽  
Theoretical Computer ◽  
Combinatorial Optimization Problems ◽  
Hard Problems ◽  
Problem Instances ◽  
Annealing Algorithms ◽  
D Wave

AbstractQuantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP − hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.

scholarly journals Constructive Genetic Algorithm for Clustering Problems

2001 ◽  
Vol 9 (3) ◽  
pp. 309-327 ◽  
Author(s):  
Luiz Antonio Nogueira Lorena ◽  
João Carlos Furtado
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Positive Influence ◽  
Greedy Heuristics ◽  
Fitness Functions ◽  
Common Basis ◽  
Rejection Threshold ◽  
Block Construction ◽  
Problem Instances ◽  
Clustering Problems

Genetic algorithms (GAs) have recently been accepted as powerful approaches to solving optimization problems. It is also well-accepted that building block construction (schemata formation and conservation) has a positive influence on GA behavior. Schemata are usually indirectly evaluated through a derived structure. We introduce a new approach called the Constructive Genetic Algorithm (CGA), which allows for schemata evaluation and the provision of other new features to the GA. Problems are modeled as bi-objective optimization problems that consider the evaluation of two fitness functions. This double fitness process, called fg-fitness, evaluates schemata and structures in a common basis. Evolution is conducted considering an adaptive rejection threshold that contemplates both objectives and attributes a rank to each individual in population. The population is dynamic in size and composed of schemata and structures. Recombination preserves good schemata, and mutation is applied to structures to get population diversification. The CGA is applied to two clustering problems in graphs. Representation of schemata and structures use a binary digit alphabet and are based on assignment (greedy) heuristics that provide a clearly distinguished representation for the problems. The clustering problems studied are the classical p-median and the capacitated p-median. Good results are shown for problem instances taken from the literature.

scholarly journals Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

2017 ◽  
Author(s):  
Christos Papalitsas ◽  
Panayiotis Karakostas ◽  
Theodore Andronikos ◽  
Spyros Sioutas ◽  
Konstantinos Giannakis
Keyword(s):  
Variable Neighborhood Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Real Life ◽  
Neighborhood Search ◽  
Np Hard ◽  
Combinatorial Optimization Problems ◽  
Np Hard Problem ◽  
Gps System ◽  
Tools And Techniques

General Variable Neighborhood Search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. Quantum General Variable Neighborhood Search (qGVNS) is a novel, quantum inspired extension of the conventional GVNS. Its quantum nature derives from the fact that it takes advantage and incorporates tools and techniques from the field of quantum computation. Travelling Salesman Problem (TSP) is a well known NP-Hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes for Geographical Systems (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of symmetric TSP instances (symmetric in order to faithfully simulate GPS problems), which are shown in a series of figures and tables, allow us to conclude that the novel qGVNS algorithm can provide an efficient solution for this type of geographical problems.

COMPUTATIONAL METHODS FOR LOGISTICS PROBLEMS RELATED TO OPTIMAL TREES

2017 ◽  
Vol 58 (3-4) ◽  
pp. 333-341
Author(s):  
LONGSHU WU ◽  
QIN WANG ◽  
XIAOBING YANG
Keyword(s):  
Computational Methods ◽  
Network Optimization ◽  
Optimization Problems ◽  
Dominating Set ◽  
Network Models ◽  
Tree Structures ◽  
Dominating Set Problem ◽  
Optimal Tree ◽  
Optimal Trees ◽  
Balanced Network

In recent years, balanced network optimization problems play an important role in practice, especially in information transmission, industry production and logistics management. In this paper, we consider some logistics optimization problems related to the optimal tree structures in a network. We show that the most optimal subtree problem is NP-hard by transforming the connected dominating set problem into this model. By constructing the network models of the most balanced spanning tree problem with edge set restrictions, and by finding the optimal subtrees in special networks, we present efficient computational methods for solving some logistics problems.

A Linear Time Solution for N-Queens Problem Using Generalized Networks of Evolutionary Polarized Processors

2020 ◽  
Vol 31 (01) ◽  
pp. 7-21 ◽  
Author(s):  
Fernando Arroyo Montoro ◽  
Sandra Gómez-Canaval ◽  
Karina Jiménez Vega ◽  
Alfonso Ortega de la Puente
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Evaluation ◽  
Optimization Problems ◽  
Linear Time ◽  
Combinatorial Optimization Problems ◽  
New Variant ◽  
Generalized Networks ◽  
Relevant Role ◽  
Np Hard Problem ◽  
Hard Problems

In this paper we consider a new variant of Networks of Polarized Evolutionary Processors (NPEP) named Generalized Networks of Evolutionary Polarized Processors (GNPEP) and propose them as solvers of combinatorial optimization problems. Unlike the NPEP model, GNPEP uses its numerical evaluation over the processed data from a quantitative perspective, hence this model might be more suitable to solve specific hard problems in a more efficient and economic way. In particular, we propose a GNPEP network to solve a well-known NP-hard problem, namely the [Formula: see text]-queens. We prove that this GNPEP algorithm requires a linear time in the size of a given instance. This result suggests that the GNPEP model is more suitable to address problems related to combinatorial optimization in which integer restrictions have a relevant role.

scholarly journals An Improved Greedy Heuristic for the Minimum Positive Influence Dominating Set Problem in Social Networks

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 79
Author(s):  
Salim Bouamama ◽  
Christian Blum
Keyword(s):  
Social Networks ◽  
Greedy Algorithm ◽  
Dominating Set ◽  
Positive Influence ◽  
Greedy Heuristic ◽  
Greedy Heuristics ◽  
Small Subset ◽  
Problem Size ◽  
Wide Range ◽  
Dominating Set Problem

This paper presents a performance comparison of greedy heuristics for a recent variant of the dominating set problem known as the minimum positive influence dominating set (MPIDS) problem. This APX-hard combinatorial optimization problem has applications in social networks. Its aim is to identify a small subset of key influential individuals in order to facilitate the spread of positive influence in the whole network. In this paper, we focus on the development of a fast and effective greedy heuristic for the MPIDS problem, because greedy heuristics are an essential component of more sophisticated metaheuristics. Thus, the development of well-working greedy heuristics supports the development of efficient metaheuristics. Extensive experiments conducted on a wide range of social networks and complex networks confirm the overall superiority of our greedy algorithm over its competitors, especially when the problem size becomes large. Moreover, we compare our algorithm with the integer linear programming solver CPLEX. While the performance of CPLEX is very strong for small and medium-sized networks, it reaches its limits when being applied to the largest networks. However, even in the context of small and medium-sized networks, our greedy algorithm is only 2.53% worse than CPLEX.

Solving Graph Coloring Problem Using an Enhanced Binary Dragonfly Algorithm

2019 ◽  
Vol 10 (3) ◽  
pp. 23-45 ◽  
Author(s):  
Karim Baiche ◽  
Yassine Meraihi ◽  
Manolo Dulva Hina ◽  
Amar Ramdane-Cherif ◽  
Mohammed Mahseur
Keyword(s):  
Graph Coloring ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Random Parameters ◽  
Dragonfly Algorithm ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Graph Coloring Problem ◽  
Np Hard Problem ◽  
The Right

The graph coloring problem (GCP) is one of the most interesting classical combinatorial optimization problems in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. In this article, the authors propose a new enhanced binary dragonfly algorithm to solve the graph coloring problem. The binary dragonfly algorithm has been enhanced by introducing two modifications. First, the authors use the Gaussian distribution random selection method for choosing the right value of the inertia weight w used to update the step vector (∆X). Second, the authors adopt chaotic maps to determine the random parameters s, a, c, f, and e. The aim of these modifications is to improve the performance and the efficiency of the binary dragonfly algorithm and ensure the diversity of solutions. The authors consider the well-known DIMACS benchmark graph coloring instances to evaluate the performance of their algorithm. The simulation results reveal the effectiveness and the successfulness of the proposed algorithm in comparison with some well-known algorithms in the literature.

scholarly journals Integrating Pseudo-Boolean Constraint Reasoning in Multi-Objective Evolutionary Algorithms

2019 ◽  
Author(s):  
Miguel Terra-Neves ◽  
Inês Lynce ◽  
Vasco Manquinho
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
State Of The Art ◽  
Solution Space ◽  
Problem Instance ◽  
Multi Objective ◽  
Constraint Reasoning ◽  
Problem Instances ◽  
Quality Of The Population

Constraint-based reasoning methods thrive in solving problem instances with a tight solution space. On the other hand, evolutionary algorithms are usually effective when it is not hard to satisfy the problem constraints. This dichotomy has been observed in many optimization problems. In the particular case of Multi-Objective Combinatorial Optimization (MOCO), new recently proposed constraint-based algorithms have been shown to outperform more established evolutionary approaches when a given problem instance is hard to satisfy. In this paper, we propose the integration of constraint-based procedures in evolutionary algorithms for solving MOCO. First, a new core-based smart mutation operator is applied to individuals that do not satisfy all problem constraints. Additionally, a new smart improvement operator based on Minimal Correction Subsets is used to improve the quality of the population. Experimental results clearly show that the integration of these operators greatly improves multi-objective evolutionary algorithms MOEA/D and NSGAII. Moreover, even on problem instances with a tight solution space, the newly proposed algorithms outperform the state-of-the-art constraint-based approaches for MOCO.

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