Applications of Bee Colony Optimization

Many computationally difficult problems are attacked using non-exact algorithms, such as approximation algorithms and heuristics. This thesis investigates an ex- ample of the latter, Bee Colony Optimization, on both an established optimization problem in the form of the Quadratic Assignment Problem and the FireFighting problem, which has not been studied before as an optimization problem. Bee Colony Optimization is a swarm intelligence algorithm, a paradigm that has increased in popularity in recent years, and many of these algorithms are based on natural pro- cesses. We tested the Bee Colony Optimization algorithm on the QAPLIB library of Quadratic Assignment Problem instances, which have either optimal or best known solutions readily available, and enabled us to compare the quality of solutions found by the algorithm. In addition, we implemented a couple of other well known algorithms for the Quadratic Assignment Problem and consequently we could analyse the runtime of our algorithm. We introduce the Bee Colony Optimization algorithm for the FireFighting problem. We also implement some greedy algorithms and an Ant Colony Optimization al- gorithm for the FireFighting problem, and compare the results obtained on some randomly generated instances. We conclude that Bee Colony Optimization finds good solutions for the Quadratic Assignment Problem, however further investigation on speedup methods is needed to improve its performance to that of other algorithms. In addition, Bee Colony Optimization is effective on small instances of the FireFighting problem, however as instance size increases the results worsen in comparison to the greedy algorithms, and more work is needed to improve the decisions made on these instances

Performance tradeoffs in static and dynamic load balancing strategies

The problem of uniformly distributing the load of a parallel program over a multiprocessor system was considered. A program was analyzed whose structure permits the computation of the optimal static solution. Then four strategies for load balancing were described and their performance compared. The strategies are: (1) the optimal static assignment algorithm which is guaranteed to yield the best static solution, (2) the static binary dissection method which is very fast but sub-optimal, (3) the greedy algorithm, a static fully polynomial time approximation scheme, which estimates the optimal solution to arbitrary accuracy, and (4) the predictive dynamic load balancing heuristic which uses information on the precedence relationships within the program and outperforms any of the static methods. It is also shown that the overhead incurred by the dynamic heuristic is reduced considerably if it is started off with a static assignment provided by either of the other three strategies

Energy-Efficient Heterogeneous Cellular Networks with Spectrum Underlay and Overlay Access

In this paper, we provide joint subcarrier assignment and power allocation schemes for quality-of-service (QoS)-constrained energy-efficiency (EE) optimization in the downlink of an orthogonal frequency division multiple access (OFDMA)-based two-tier heterogeneous cellular network (HCN). Considering underlay transmission, where spectrum-efficiency (SE) is fully exploited, the EE solution involves tackling a complex mixed-combinatorial and non-convex optimization problem. With appropriate decomposition of the original problem and leveraging on the quasi-concavity of the EE function, we propose a dual-layer resource allocation approach and provide a complete solution using difference-of-two-concave-functions approximation, successive convex approximation, and gradient-search methods. On the other hand, the inherent inter-tier interference from spectrum underlay access may degrade EE particularly under dense small-cell deployment and large bandwidth utilization. We therefore develop a novel resource allocation approach based on the concepts of spectrum overlay access and resource efficiency (RE) (normalized EE-SE trade-off). Specifically, the optimization procedure is separated in this case such that the macro-cell optimal RE and corresponding bandwidth is first determined, then the EE of small-cells utilizing the remaining spectrum is maximized. Simulation results confirm the theoretical findings and demonstrate that the proposed resource allocation schemes can approach the optimal EE with each strategy being superior under certain system settings

Approximating the problem, not the solution: An alternative view of point set matching

This work discusses the issue of approximation in point set matching. In general, one may have two classes of approximations when tackling a matching problem: (1) an algorithmic approximation which consists in using suboptimal procedures to infer the assignment, and (2), a representational approximation which involves a simplified and suboptimal model for the original data. Matching techniques have typically relied on the first approach by retaining the complete model and using suboptimal techniques to solve it. In this paper, we show how a technique based on using exact inference in simple Graphical Models, an instance of the second class, can significantly outperform instances of techniques from the first class. We experimentally compare this method with well-known Spectral and Relaxation methods, which are exemplars of the first class. We have performed experiments with synthetic and real-world data sets which reveal significant performance improvement in a wide operating range

Autonomous Guidance Strategy for Spacecraft Formations and Reconfiguration Maneuvers

A guidance strategy for autonomous spacecraft formation reconfiguration maneuvers is presented. The guidance strategy is presented as an algorithm that solves the linked assignment and delivery problems. The assignment problem is the task of assigning the member spacecraft of the formation to their new positions in the desired formation geometry. The guidance algorithm uses an auction process (also called an “auction algorithm”), presented in the dissertation, to solve the assignment problem. The auction uses the estimated maneuver and time of flight costs between the spacecraft and targets to create assignments which minimize a specific “expense” function for the formation. The delivery problem is the task of delivering the spacecraft to their assigned positions, and it is addressed through one of two guidance schemes described in this work. The first is a delivery scheme based on artificial potential function (APF) guidance. APF guidance uses the relative distances between the spacecraft, targets, and any obstacles to design maneuvers based on gradients of potential fields. The second delivery scheme is based on model predictive control (MPC); this method uses a model of the system dynamics to plan a series of maneuvers designed to minimize a unique cost function. The guidance algorithm uses an analytic linearized approximation of the relative orbital dynamics, the Yamanaka-Ankersen state transition matrix, in the auction process and in both delivery methods. The proposed guidance strategy is successful, in simulations, in autonomously assigning the members of the formation to new positions and in delivering the spacecraft to these new positions safely using both delivery methods. This guidance algorithm can serve as the basis for future autonomous guidance strategies for spacecraft formation missions

An agile vehicle-based dynamic user equilibrium scheme for urban traffic signal control

Traffic Signal Control (TSC) is a fundamental task in modern intelligent transport systems. TSC is often formulated as a bi-level optimization problem, comprised by the signal timing at the upper level and the Dynamic User Equilibrium (DUE) traffic assignment at the lower level. Since DUE is non-convex, existing methods either formulate approximation models or adopt traffic simulators. However, approximation models may oversimplify the practical situations, while traffic simulators are usually time-consuming. This paper formulates a vehicle-based DUE (vDUE) model and proposes an agile method that can simultaneously maintain the computational simplicity and the traffic dynamics for the traffic assignment. Further, an agile TSC system is built by combining the vDUE at the lower level for the traffic assignment with an adaptive differential evolution algorithm at the upper level for the signal timing optimization. To enhance the effectiveness of optimization, the TSC problem formulation is also improved to make it better characterize the practical requirements. In the experiments undertaken, comparisons of different TSC methods are carried out on both real-world and synthetic transportation networks. The experimental results validate the effectiveness of the proposed agile TSC system in various traffic situations

On Minimizing the Makespan When Some Jobs Cannot Be Assigned on the Same Machine

We study the classical scheduling problem of assigning jobs to machines in order to minimize the makespan. It is well-studied and admits an EPTAS on identical machines and a (2-1/m)-approximation algorithm on unrelated machines. In this paper we study a variation in which the input jobs are partitioned into bags and no two jobs from the same bag are allowed to be assigned on the same machine. Such a constraint can easily arise, e.g., due to system stability and redundancy considerations. Unfortunately, as we demonstrate in this paper, the techniques of the above results break down in the presence of these additional constraints. Our first result is a PTAS for the case of identical machines. It enhances the methods from the known (E)PTASs by a finer classification of the input jobs and careful argumentations why a good schedule exists after enumerating over the large jobs. For unrelated machines, we prove that there can be no (log n)^{1/4-epsilon}-approximation algorithm for the problem for any epsilon > 0, assuming that NP nsubseteq ZPTIME(2^{(log n)^{O(1)}}). This holds even in the restricted assignment setting. However, we identify a special case of the latter in which we can do better: if the same set of machines we give an 8-approximation algorithm. It is based on rounding the LP-relaxation of the problem in phases and adjusting the residual fractional solution after each phase to order to respect the bag constraints

Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on solving the assignment problem, a special case of optimal transport, for all consecutive timesteps. Our approach relies on two main contributions. First, we revisit the seminal assignment algorithm by Kuhn and Munkres which we specifically adapt to the problem of matching persistence diagrams in an efficient way. Second, we propose an extension of the Wasserstein metric that significantly improves the geometrical stability of the matching of domain-embedded persistence pairs. We show that this geometrical lifting has the additional positive side-effect of improving the assignment matrix sparsity and therefore computing time. The global framework implements a coarse-grained parallelism by computing persistence diagrams and finding optimal matchings in parallel for every couple of consecutive timesteps. Critical trajectories are constructed by associating successively matched persistence pairs over time. Merging and splitting events are detected with a geometrical threshold in a post-processing stage. Extensive experiments on real-life datasets show that our matching approach is an order of magnitude faster than the seminal Munkres algorithm. Moreover, compared to a modern approximation method, our method provides competitive runtimes while yielding exact results. We demonstrate the utility of our global framework by extracting critical point trajectories from various simulated time-varying datasets and compare it to the existing methods based on associated overlaps of volumes. Robustness to noise and temporal resolution downsampling is empirically demonstrated