Yiu-Wing Leung

An orthogonal genetic algorithm with quantization for global numerical optimization

We design a genetic algorithm called the orthogonal genetic algorithm with quantization for global numerical optimization with continuous variables. Our objective is to apply methods of experimental design to enhance the genetic algorithm, so that the resulting algorithm can be more robust and statistically sound. A quantization technique is proposed to complement an experimental design method called orthogonal design. We apply the resulting methodology to generate an initial population of points that are scattered uniformly over the feasible solution space, so that the algorithm can evenly scan the feasible solution space once to locate good points for further exploration in subsequent iterations. In addition, we apply the quantization technique and orthogonal design to tailor a new crossover operator, such that this crossover operator can generate a small, but representative sample of points as the potential offspring. We execute the proposed algorithm to solve 15 benchmark problems with 30 or 100 dimensions and very large numbers of local minima. The results show that the proposed algorithm can find optimal or close-to-optimal solutions.

An orthogonal genetic algorithm for multimedia multicast routing

Many multimedia communication applications require a source to send multimedia information to multiple destinations through a communication network. To support these applications, it is necessary to determine a multicast tree of minimal cost to connect the source node to the destination nodes subject to delay constraints on multimedia communication. This problem is known as multimedia multicast routing and has been proved to be NP-complete. The paper proposes an orthogonal genetic algorithm for multimedia multicast routing. Its salient feature is to incorporate an experimental design method called orthogonal design into the crossover operation. As a result, it can search the solution space in a statistically sound manner and it is well suited for parallel implementation and execution. We execute the orthogonal genetic algorithm to solve two sets of benchmark test problems. The results indicate that for practical problem sizes, the orthogonal genetic algorithm can find near optimal solutions within moderate numbers of generations.

Multiobjective programming using uniform design and genetic algorithm

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.

Improved possibilistic C-means clustering algorithms

A possibilistic approach was proposed in a previous paper for C-means clustering, and two algorithms realizing this approach were reported in two previous papers. Although the possibilistic approach is sound, these two algorithms tend to find identical clusters. In this paper, we modify and improve these algorithms to overcome their shortcoming. The numerical results demonstrate that the improved algorithms can determine proper clusters and they can realize the advantages of the possibilistic approach.

Jump-stay based channel-hopping algorithm with guaranteed rendezvous for cognitive radio networks

Cognitive radio networks (CRNs) have emerged as advanced and promising paradigm to exploit the existing wireless spectrum opportunistically. It is crucial for users in CRNs to search for neighbors via rendezvous process and thereby establish the communication links to exchange the information necessary for spectrum management and channel contention etc. This paper focuses on the design of algorithms for blind rendezvous, i.e., rendezvous without using any central controller and common control channel (CCC). We propose a jump-stay based channel-hopping (CH) algorithm for blind rendezvous. The basic idea is to generate CH sequence in rounds and each round consists of a jump-pattern and a stay-pattern. Users “jump” on available channels in the jump-pattern while “stay” on a specific channel in the stay-pattern. Compared with the existing CH algorithms, our algorithm achieves the following advances: i) guaranteed rendezvous without the need of time-synchronization; ii) applicability to rendezvous of multi-user and multi-hop scenarios. We derive the maximum time-to-rendezvous (TTR) and the upper-bound of expected TTR of our algorithm for both 2-user and multi-user scenarios (shown in Table I). Extensive simulations are further conducted to evaluate performance of our algorithm.

Jump-Stay Rendezvous Algorithm for Cognitive Radio Networks

Cognitive radio networks (CRNs) have emerged as advanced and promising paradigm to exploit the existing wireless spectrum opportunistically. It is crucial for users in CRNs to search for neighbors via rendezvous process and thereby establish the communication links to exchange the information necessary for spectrum management and channel contention, etc. This paper focuses on the design of algorithms for blind rendezvous, i.e., rendezvous without using any centralized controller and common control channel (CCC). We propose a jump-stay channel-hopping (CH) algorithm for blind rendezvous. The basic idea is to generate CH sequence in rounds and each round consists of a jump-pattern and a stay-pattern. Users “jump” on available channels in the jump-pattern while “stay” on a specific channel in the stay-pattern. We prove that two users can achieve rendezvous in one of four possible pattern combinations: jump-stay, stay-jump, jump-jump, and stay-stay. Compared with the existing CH algorithms, our algorithm has the overall best performance in various scenarios and is applicable to rendezvous of multiuser and multihop scenarios. We derive upper bounds on the maximum time-to-rendezvous (TTR) and the expected TTR of our algorithm for both 2-user and multiuser scenarios (shown in Table 1). Extensive simulations are conducted to evaluate the performance of our algorithm.

Algorithms for allocating wavelength converters in all-optical networks

In an all-optical wide area network, some network nodes may handle heavier volumes of traffic. It is desirable to allocate more full-range wavelength converters (FWCs) to these nodes, so that the FWCs can be fully utilized to resolve wavelength conflict. We propose a set of algorithms for allocating FWCs in all-optical networks. We adopt the simulation-based optimization approach, in which we collect utilization statistics of FWCs from computer simulations and then perform optimization to allocate the FWCs. Therefore, our algorithms are widely applicable and they are not restricted to any particular model or assumption. We have conducted extensive computer simulations on regular and irregular networks under both uniform and nonuniform traffic. Compared with the best existing allocation, the results show that our algorithms can significantly reduce: (1) the overall blocking probability (i.e., better mean quality of service) and (2) the maximum of the blocking probabilities experienced at all the source nodes (i.e., better fairness). Equivalently, for a given performance requirement on blocking probability, our algorithms can significantly reduce the number of FWCs required.

Enhanced Jump-Stay Rendezvous Algorithm for Cognitive Radio Networks

Rendezvous is a fundamental operation for cognitive users to establish communication links. In [5], we proposed a jump-stay (JS) rendezvous algorithm which was shown to have the overall best performance. In this work, we propose an enhanced jump-stay (EJS) algorithm. Compared with JS, EJS lowers the upper-bounds of both the maximum time-to-rendezvous (MTTR) and the expected time-to-rendezvous (E(TTR)) from O(P3) to O(P2) under the asymmetric model, while keeping the same order O(P) of upper-bounds of MTTR and E(TTR) under the symmetric mode, where P is the smallest prime number greater than the total number of channels.

U-measure: a quality measure for multiobjective programming

A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and so their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier. This frontier is a nonlinear hyper-surface. We measure the uniformity over this hyper-surface in three main steps: 1) determine the domains of the Pareto frontier over which uniformity is measured, 2) determine the nearest neighbors of each solution in the objective space, and 3) compute the discrepancy among the distances between nearest neighbors. The U-measure is equal to this discrepancy where a smaller discrepancy indicates a better uniformity. We can apply the U-measure to complement the other quality measures so that we can evaluate and compare multiobjective programming algorithms from different perspectives.

Simple movement control algorithm for bi-connectivity in robotic sensor networks

Robotic sensor networks are more powerful than sensor networks because the sensors can be moved by the robots to adjust their sensing coverage. In robotic sensor networks, an important problem is movement control: how the robots can autonomously move to the desired locations for sensing and data collection. In this paper, we study a new movement control problem with the following essential requirements: i) an initial and possibly disconnected network is self-organized into a bi-connected network, ii) only 1-hop information is used for movement control, iii) the coverage of the network is maximized while the total moving distance in the movement process is minimized. We propose a simple movement control algorithm for this problem. This algorithm emulates the attractive force (such as the force in a stretched spring) and the repulsive force (such as the electrostatic force between electric charges) in nature, such that each robot simply follows the resultant virtual force to move. We theoretically prove that this algorithm guarantees bi-connected networks under a mild condition and derive bounds on the maximum coverage and the minimum moving distance. We conduct extensive simulation experiments to demonstrate that the proposed algorithm is effective.