Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

An investigation of multilevel refinement in routing and location problems

Multilevel refinement is a collaborative hierarchical solution technique. The multilevel technique aims to enhance the solution process of optimisation problems by improving the asymptotic convergence in the quality of solutions produced by its underlying local search heuristics and/or improving the convergence rate of these heuristics. To these aims, the central methodologies of the multilevel technique are filtering solutions from the search space (via coarsening), reducing the amount of problem detail considered at each level of the solution process and providing a mechanism to the underlying local search heuristics for efficiently making large moves around the search space. The neighbourhoods accessible by these moves are typically inaccessible if the local search heuristics are applied to the un-coarsened problems. The methodologies combine to meet the multilevel technique's aims, because, as the multilevel technique iteratively coarsens, extends and refines a given problem, it reduces the possibility of the local search heuristic becoming trapped in local optima of poor quality. The research presented in this thesis investigates the application of multilevel refinement to classes of location and routing problems and develops numerous multilevel algorithms. Some of these algorithms are collaborative techniques for metaheuristics and others are collaborative techniques for local search heuristics. Additionally, new methods of coarsening for location and routing problems and enhancements for the multilevel technique are developed. It is demonstrated that the multilevel technique is suited to a wide array of problems. By extending the investigations of the multilevel technique across routing and location problems, the research was able to present generalisations regarding the multilevel technique's suitability, for these and similar types of problems. Finally, results on a number of well known benchmarking suites for location and routing problem are presented, comparing equivalent single-level and multilevel algorithms. These results demonstrate that the multilevel technique provides significant gains over its single-level counterparts. In all cases, the multilevel algorithm was able to improve the asymptotic convergence in the quality of solutions produced by the standard (single-level) local search heuristics or metaheuristics. The multilevel technique did not improve the convergence rate of the single-level's local search heuristics in all cases. However, for large-scale problems the multilevel variants scaled in a manner superior to the single-level techniques. The research also demonstrated that for sufficiently large problems, the multilevel technique was able to improve the asymptotic convergence in the quality of solutions at a sufficiently fast rate, such that the multilevel algorithms were able to produce superior results compared to the single-level versions, without refining the solution down to the most detailed level

Revisiting the Evolution and Application of Assignment Problem: A Brief Overview

The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on   a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Using Stigmergy to Solve Numerical Optimization Problems

The current methodology for designing highly efficient technological systems needs to choose the best combination of the parameters that affect the performance. In this paper we propose a promising optimization algorithm, referred to as the Multilevel Ant Stigmergy Algorithm (MASA), which exploits stigmergy in order to optimize multi-parameter functions. We evaluate the performance of the MASA and Differential Evolution -- one of the leading stochastic method for numerical optimization -- in terms of their applicability as numerical optimization techniques. The comparison is performed using several widely used benchmark functions with added noise