Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP where 1 stands for a node being selected to construct the multicast tree while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on GA, ACO, and PSO

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

A genetic algorithm for power distribution system planning

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.The planning of distribution systems consists in determining the optimum site and size of new substations and feeders in order to satisfy the future power demand with minimum investment and operational costs and an acceptable level of reliability. This problem is a combinatorial, non-linear and constrained optimization problem. Several solution methods based on genetic algorithms have been reported in the literature; however, some of these methods have been reported with applications to small systems while others have long solution time. In addition, the vast majority of the developed methods handle planning problems simplifying them as single-objective problems but, there are some planning aspects that can not be combined into a single scalar objective; therefore, they require to be treated separately. The cause of these shortcomings is the poor representation of the potential solutions and their genetic operators This thesis presents the design of a genetic algorithm using a direct representation technique and specialized genetic operators for power distribution system expansion planning problems. These operators effectively preserve and exploit critical configurations that contribute to the optimization of the objective function. The constraints of the problems are efficiently handle with new strategies. The genetic algorithm was tested on several theoretical and real large-scale power distribution systems. Problems of network reconfiguration for loss reduction were also included in order to show the potential of the algorithm to resolve operational problems. Both single-objective and multi-objective formulations were considered in the tests. The results were compared with results from other heuristic methods such as ant colony system algorithms, evolutionary programming, differential evolution and other genetic algorithms reported in the literature. From these comparisons it was concluded that the proposed genetic algorithm is suitable to resolve problems of largescale power distribution system planning. Moreover, the algorithm proved to be effective, efficient and robust with better performance than other previous methods.National Council for Science and Technology, Mexic

Multi-objective optimal design of obstacle-avoiding two-dimensional Steiner trees with application to ascent assembly engineering.

We present an effective optimization strategy that is capable of discovering high-quality cost-optimal solution for two-dimensional (2D) path network layouts (i.e., groups of obstacle-avoiding Euclidean Steiner trees) that, among other applications, can serve as templates for complete ascent assembly structures (CAA-structures). The main innovative aspect of our approach is that our aim is not restricted to simply synthesizing optimal assembly designs with regard to a given goal, but we also strive to discover the best trade-offs between geometric and domain-dependent optimal designs. As such, the proposed approach is centred on a variably constrained multi-objective formulation of the optimal design task and on an efficient co-evolutionary solver. The results we obtained on both artificial problems and realistic design scenarios based on an industrial test case empirically support the value of our contribution to the fields of optimal obstacle-avoiding path generation in particular and design automation in general

Optimizing and Reoptimizing: tackling static and dynamic combinatorial problems

As suggested by the title, in this thesis both static and dynamic problems of Operations Research will be addressed by either designing new procedures or adapting well-known algorithmic schemes. Specifically, the first part of the thesis is devoted to the discussion of three variants of the widely studied Shortest Path Problem, one of which is defined on dynamic graphs. Namely, first the Reoptimization of Shortest Paths in case of multiple and generic cost changes is dealt with an exact algorithm whose performance is compared with Dijkstra's label setting procedure in order to detect which approach has to be preferred. Secondly, the k-Color Shortest Path Problem is tackled. It is a recent problem, defined on an edge-constrained graph, for which a Dynamic Programming algorithm is proposed here; its performance is compared with the state of the art solution approach, namely a Branch & Bound procedure. Finally, the Resource Constrained Clustered Shortest Path Tree Problem is presented. It is a newly defined problem for which both a mathematical model and a Branch & Price procedure are detailed here. Moreover, the performance of this solution approach is compared with that of CPLEX solver. Furthermore, in the first part of the thesis, also the Path Planning in Urban Air Mobility, is discussed by considering both the definition of the Free-Space Maps and the computation of the trajectories. For the former purpose, three different but correlated discretization methods are described; as for the latter, a two steps resolution, offline and online, of the resulting shortest path problems is performed. In addition, it is checked whether the reoptimization algorithm can be used in the online step. In the second part of this thesis, the recently studied Additive Manufacturing Machine Scheduling Problem with not identical machines is presented. Specifically, a Reinforcement Learning Iterated Local Search meta-heuristic featuring a Q-learning Variable Neighbourhood Search is described to solve this problem and its performance is compared with the one of CPLEX solver. It is worthwhile mentioning that, for each of the proposed approaches, a thorough experimentation is performed and each Chapter is equipped with a detailed analysis of the results in order to appraise the performance of the method and to detect its limits