A Multilevel Evolutionary Algorithm Applied to the Maximum Satisfiability Problems

The maximum satisfiability problem that is known to be nondeterministic polynomial (NP) complete plays a central role problem in many applications in the fields of very large-scale integration (VLSI) computer-aided design, computing theory, artificial intelligence, and defense. Given a set of m clauses and n Boolean variables, the maximum satisfiability problem refers to the task of finding an assignment of values to the variables that maximizes the number of satisfied clauses (or minimizes the number of unsatisfied clauses) In this chapter, a multilevel evolutionary algorithm is proposed for the maximum satisfiability problem. The multilevel process works by grouping the variables defining the problem to form clusters, uses the clusters to define a new problem, and is repeated until the problem size falls below some threshold. The coarsest problem is then given an initial assignment of values to variables and the assignment is successively refined on all the problems starting with the coarsest and ending with the original

Towards a multilevel ant colony optimization

Masteroppgave i Informasjons- og kommunikasjonsteknologi IKT590 Universitetet i Agder 2014Ant colony optimization is a metaheuristic approach for solving combinatorial optimization problems which belongs to swarm intelligence techniques. Ant colony optimization algorithms are one of the most successful strands of swarm intelligence which has already shown very good performance in many combinatorial problems and for some real applications. This thesis introduces a new multilevel approach for ant colony optimization to solve the NP-hard problems shortest path and traveling salesman. We have reviewed different elements of multilevel algorithm which helped us in construction of our proposed multilevel ant colony optimization solution. We for comparison purposes implemented our own multi-threaded variant Dijkstra for solving shortest path to compare it with single level and multilevel ant colony optimization and reviewed different techniques such as genetic algorithms and Dijkstra’s algorithm. Our proposed multilevel ant colony optimization was developed based on the single level ant colony optimization which we both implemented. We have applied the novel multilevel ant colony optimization to solve the shortest path and traveling salesman problem. We show that the multilevel variant of ant colony optimization outperforms single level. The experimental results conducted demonstrate the overall performance of multilevel in comparison to the single level ant colony optimization, displaying a vast improvement when employing a multilevel approach in contrast to the classical single level approach. These results gave us a better understanding of the problems and provide indications for further research

Graph partitioning algorithms for optimizing software deployment in mobile cloud computing

As cloud computing is gaining popularity, an important question is how to optimally deploy software applications on the offered infrastructure in the cloud. Especially in the context of mobile computing where software components could be offloaded from the mobile device to the cloud, it is important to optimize the deployment, by minimizing the network usage. Therefore we have designed and evaluated graph partitioning algorithms that allocate software components to machines in the cloud while minimizing the required bandwidth. Contrary to the traditional graph partitioning problem our algorithms are not restricted to balanced partitions and take into account infrastructure heterogenity. To benchmark our algorithms we evaluated their performance and found they produce 10 to 40 % smaller graph cut sizes than METIS 4.0 for typical mobile computing scenarios

Quantum and Classical Multilevel Algorithms for (Hyper)Graphs

Combinatorial optimization problems on (hyper)graphs are ubiquitous in science and industry. Because many of these problems are NP-hard, development of sophisticated heuristics is of utmost importance for practical problems. In recent years, the emergence of Noisy Intermediate-Scale Quantum (NISQ) computers has opened up the opportunity to dramaticaly speedup combinatorial optimization. However, the adoption of NISQ devices is impeded by their severe limitations, both in terms of the number of qubits, as well as in their quality. NISQ devices are widely expected to have no more than hundreds to thousands of qubits with very limited error-correction, imposing a strict limit on the size and the structure of the problems that can be tackled directly. A natural solution to this issue is hybrid quantum-classical algorithms that combine a NISQ device with a classical machine with the goal of capturing “the best of both worlds”. Being motivated by lack of high quality optimization solvers for hypergraph partitioning, in this thesis, we begin by discussing classical multilevel approaches for this problem. We present a novel relaxation-based vertex similarity measure termed algebraic distance for hypergraphs and the coarsening schemes based on it. Extending the multilevel method to include quantum optimization routines, we present Quantum Local Search (QLS) – a hybrid iterative improvement approach that is inspired by the classical local search approaches. Next, we introduce the Multilevel Quantum Local Search (ML-QLS) that incorporates the quantum-enhanced iterative improvement scheme introduced in QLS within the multilevel framework, as well as several techniques to further understand and improve the effectiveness of Quantum Approximate Optimization Algorithm used throughout our work

MULTILEVEL ANT COLONY OPTIMIZATION TO SOLVE CONSTRAINED FOREST TRANSPORTATION PLANNING PROBLEMS

In this dissertation, we focus on solving forest transportation planning related problems, including constraints that consider negative environmental impacts and multi-objective optimizations that provide forest managers and road planers alternatives for making informed decisions. Along this line of study, several multilevel techniques and mataheuristic algorithms have been developed and investigated. The forest transportation planning problem is a fixed-charge problem and known to be NP-hard. The general idea of utilizing multilevel approach is to solve the original problem of which the computational cost maybe prohibitive by using a set of increasingly smaller problems of which the computational cost is cheaper. The multilevel techniques are devised consisting of two parts. The first part is to recursively apply a graph coarsening heuristic to the original problem to produce a set of coarser level problems of which the sizes in terms of number of problem components such as edges and nodes are in decreasing order. The second part is to solve the set of the coarser level problems including the original problem bottom up, starting with the coarsest level. We propose that if coarser level problems inherit important properties (such as attribute value distribution) from their ancestor during the coarsening process, they can be treated as smaller versions of the original problem. Based on this hypothesis, the multilevel techniques use solutions obtained for the coarser level problems to solve the finer level problems. Mainly, we develop multilevel techniques to address three problems, namely a constrained fixed-charge problem, parameter configuration problem, and a multi-objective transportation optimization problem in this study. The performance of the multilevel techniques is compared with other commonly used approaches. The statistical analyses on the experimental results indicate that the multilevel approach can reduce computing time significantly without sacrificing the solution quality