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We investigate a family of $(\mu+\lambda)$ Genetic Algorithms (GAs) which creates offspring either from mutation or by recombining two randomly chosen parents. By scaling the crossover probability, we can thus interpolate from a fully…
This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
Predicting the cheapest sample size for the optimal stratification in multivariate survey design is a problem in cases where the population frame is large. A solution exists that iteratively searches for the minimum sample size necessary to…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…
Block scheduling is difficult to implement in P2P network since there is no central coordinator. This problem can be solved by employing network coding technique which allows intermediate nodes to perform the coding operation instead of…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it…
We introduce the Multicolored Graph Realization problem (MGRP). The input to the problem is a colored graph $(G,\varphi)$, i.e., a graph together with a coloring on its vertices. We can associate to each colored graph a cluster graph…
In this paper, we apply the Rank-Sparsity Matrix Decomposition to the planted Maximum Quasi-Clique Problem (MQCP). This problem has the planted Maximum Clique Problem (MCP) as a special case. The maximum clique problem is NP-hard. A…
The 0-1 Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact…
We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination…
Graph problems are troublesome when it comes to MapReduce. Typically, to be able to design algorithms that make use of the advantages of MapReduce, assumptions beyond what the model imposes, such as the density of the input graph, are…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…