Xiao-Bing Hu

Calculating Complete and Exact Pareto Front for Multiobjective Optimization: A New Deterministic Approach for Discrete Problems

Searching the Pareto front for multiobjective optimization problems usually involves the use of a population-based search algorithm or of a deterministic method with a set of different single aggregate objective functions. The results are, in fact, only approximations of the real Pareto front. In this paper, we propose a new deterministic approach capable of fully determining the real Pareto front for those discrete problems for which it is possible to construct optimization algorithms to find the k best solutions to each of the single-objective problems. To this end, two theoretical conditions are given to guarantee the finding of the actual Pareto front rather than its approximation. Then, a general methodology for designing a deterministic search procedure is proposed. A case study is conducted, where by following the general methodology, a ripple-spreading algorithm is designed to calculate the complete exact Pareto front for multiobjective route optimization. When compared with traditional Pareto front search methods, the obvious advantage of the proposed approach is its unique capability of finding the complete Pareto front. This is illustrated by the simulation results in terms of both solution quality and computational efficiency.

A ripple-spreading genetic algorithm for the aircraft sequencing problem

When genetic algorithms (GAs) are applied to combinatorial problems, permutation representations are usually adopted. As a result, such GAs are often confronted with feasibility and memory-efficiency problems. With the aircraft sequencing problem (ASP) as a study case, this paper reports on a novel binary-representation-based GA scheme for combinatorial problems. Unlike existing GAs for the ASP, which typically use permutation representations based on aircraft landing order, the new GA introduces a novel ripple-spreading model which transforms the original landing-order-based ASP solutions into value-based ones. In the new scheme, arriving aircraft are projected as points into an artificial space. A deterministic method inspired by the natural phenomenon of ripple-spreading on liquid surfaces is developed, which uses a few parameters as input to connect points on this space to form a landing sequence. A traditional GA, free of feasibility and memory-efficiency problems, can then be used to evolve the ripple-spreading related parameters in order to find an optimal sequence. Since the ripple-spreading model is the centerpiece of the new algorithm, it is called the ripple-spreading GA (RSGA). The advantages of the proposed RSGA are illustrated by extensive comparative studies for the case of the ASP.

Deterministic agent-based path optimization by mimicking the spreading of ripples

Inspirations from nature have contributed fundamentally to the development of evolutionary computation. Learning from the natural ripple-spreading phenomenon, this article proposes a novel ripple-spreading algorithm (RSA) for the path optimization problem (POP). In nature, a ripple spreads at a constant speed in all directions, and the node closest to the source is the first to be reached. This very simple principle forms the foundation of the proposed RSA. In contrast to most deterministic top-down centralized path optimization methods, such as Dijkstra’s algorithm, the RSA is a bottom-up decentralized agent-based simulation model. Moreover, it is distinguished from other agent-based algorithms, such as genetic algorithms and ant colony optimization, by being a deterministic method that can always guarantee the global optimal solution with very good scalability. Here, the RSA is specifically applied to four different POPs. The comparative simulation results illustrate the advantages of the RSA in terms of effectiveness and efficiency. Thanks to the agent-based and deterministic features, the RSA opens new opportunities to attack some problems, such as calculating the exact complete Pareto front in multiobjective optimization and determining the kth shortest project time in project management, which are very difficult, if not impossible, for existing methods to resolve. The ripple-spreading optimization principle and the new distinguishing features and capacities of the RSA enrich the theoretical foundations of evolutionary computation.

Multi-objective new product development by complete Pareto front and ripple-spreading algorithm

Given several different new product development projects and limited resources, this paper is concerned with the optimal allocation of resources among the projects. This is clearly a multi-objective optimization problem (MOOP), because each new product development project has both a profit expectation and a loss expectation, and such expectations vary according to allocated resources. In such a case, the goal of multi-objective new product development (MONPD) is to maximize the profit expectation while minimizing the loss expectation. As is well known, Pareto optimality and the Pareto front are extremely important to resolve MOOPs. Unlike many other MOOP methods which provide only a single Pareto optimal solution or an approximation of the Pareto front, this paper reports a novel method to calculate the complete Pareto front for the MONPD. Some theoretical conditions and a ripple-spreading algorithm together play a crucial role in finding the complete Pareto front for the MONPD. Simulation results illustrate that the reported method, by calculating the complete Pareto front, can provide the best support to decision makers in the MONPD.

A ripple-spreading Genetic Algorithm for the airport Gate Assignment Problem

Since the Gate Assignment Problem (GAP) at airport terminals is a combinatorial optimization problem, permutation representations based on aircraft dwelling orders are typically used in the implementation of Genetic Algorithms (GAs), The design of such GAs is often confronted with feasibility and memory-efficiency problems. This paper proposes a hybrid GA, which transforms the original order based GAP solutions into value based ones, so that the basic a binary representation and all classic evolutionary operations can be applied free of the above problems. In the hybrid GA scheme, aircraft queues to gates are projected as points into a parameterized space. A deterministic model inspired by the phenomenon of natural ripple-spreading on liquid surfaces is developed which uses relative spatial parameters as input to connect all aircraft points to construct aircraft queues to gates, and then a traditional binary GA compatible to all classic evolutionary operators is used to evolve these spatial parameters in order to find an optimal or near-optimal solution. The effectiveness of the new hybrid GA based on the ripple-spreading model for the GAP problem are illustrated by experiments.

Epidemic modelling by ripple-spreading network and genetic algorithm

Mathematical analysis and modelling is central to infectious disease epidemiology. This paper, inspired by the natural ripple-spreading phenomenon, proposes a novel ripple-spreading network model for the study of infectious disease transmission. The new epidemic model naturally has good potential for capturing many spatial and temporal features observed in the outbreak of plagues. In particular, using a stochastic ripple-spreading process simulates the effect of random contacts and movements of individuals on the probability of infection well, which is usually a challenging issue in epidemic modeling. Some ripple-spreading related parameters such as threshold and amplifying factor of nodes are ideal to describe the importance of individuals’ physical fitness and immunity. The new model is rich in parameters to incorporate many real factors such as public health service and policies, and it is highly flexible to modifications. A genetic algorithm is used to tune the parameters of the model by referring to historic data of an epidemic. The well-tuned model can then be used for analyzing and forecasting purposes. The effectiveness of the proposed method is illustrated by simulation results.

A Ripple-Spreading Algorithm for the k Shortest Paths Problem

Inspired by the natural ripple-spreading phenomenon that occurs on a water surface, this paper proposes a novel ripple-spreading algorithm (RSA) for the k shortest paths problem (k-SPP). In nature, a ripple spreads at a constant speed in all directions, and the node closest to the source will be the first to be reached. This very simple principle forms the foundation of the proposed RSA. By mimicking the natural ripple-spreading phenomenon, the new algorithm starts an initial ripple from the source, and initial ripple triggers new ripples at other nodes as it spreads out. A new ripple can also trigger ripples at nodes farther away, until the destination is reached by k ripples. Then the kth ripple that reaches the destination determines the kth shortest path. The comparative experimental results illustrate the effectiveness and efficiency of the proposed algorithm.

An effective genetic algorithm for network coding

The network coding problem (NCP), which aims to minimize network coding resources such as nodes and links, is a relatively new application of genetic algorithms (GAs) and hence little work has so far been reported in this area. Most of the existing literature on NCP has concentrated primarily on the static network coding problem (SNCP). There is a common assumption in work to date that a target rate is always achievable at every sink as long as coding is allowed at all nodes. In most real-world networks, such as wireless networks, any link could be disconnected at any time. This implies that every time a change occurs in the network topology, a new target rate must be determined. The SNCP software implementation then has to be re-run to try to optimize the coding based on the new target rate. In contrast, the GA proposed in this paper is designed with the dynamic network coding problem (DNCP) as the major concern. To this end, a more general formulation of the NCP is described. The new NCP model considers not only the minimization of network coding resources but also the maximization of the rate actually achieved at sinks. This is particularly important to the DNCP, where the target rate may become unachievable due to network topology changes. Based on the new NCP model, an effective GA is designed by integrating selected new problem-specific heuristic rules into the evolutionary process in order to better diversify chromosomes. In dynamic environments, the new GA does not need to recalculate target rate and also exhibits some degree of robustness against network topology changes. Comparative experiments on both SNCP and DNCP illustrate the effectiveness of our new model and algorithm.

An effective Genetic Algorithm for the network coding problem

The optimization of network coding is a relatively new area for evolutionary algorithms, as very few efforts have so far been reported. This paper is concerned with the design of an effective Genetic Algorithm (GA) for tackling the network coding problem (NCP). Differing from previous relevant works, the proposed GA is designed based on a permutation representation, which not only allows each chromosome to record a specific network protocol and coding scheme, but also makes it easy to integrate useful problem-specific heuristic rules into the algorithm. In the new GA, a more general fitness function is proposed, which, besides considering the minimization of network coding resources, also takes into account the maximization of the rate actually achieved. This new fitness function makes the proposed GA more suitable for the case of dynamic network coding, where any link could be cut off at any time, and consequently, the target rate might become unachievable even if all nodes allow coding. Based on the new representation and fitness function, other GA related techniques are modified and employed accordingly and carefully. Comparative experiments show that the proposed GA clearly outperforms previous methods.

A ripple-spreading genetic algorithm for the network coding problem

The network coding problem (NCP) is an NP-hard combinatorial problem, and genetic algorithms (GAs) have recently been applied to address this problem. This paper reports a novel ripple-spreading GA (RSGA) for the NCP. In contrast to existing GAs where a chromosome directly represents a solution, the proposed RSGA separates chromosomes and solutions by introducing a purpose-designed pre-problem for the NCP. In the pre-problem, the nodes in the NCP are projected into an artificial space, in which some ripple epicenters are randomly generated. Then a specially parameterized ripple-spreading process is employed such that as ripples (starting from the epicenters) spread out in the artificial space, the incoming signals and outgoing signals of all nodes will be individually determined, according to the amplitudes of the ripples which have reached the node. Changing the values of the ripple-spreading parameters will result in different information flows in the networks. Therefore, a simple binary-string based GA, unlike existing GAs which employ permutation representations for the NCP, can be used to optimize the values of the ripple-spreading parameters, in order to find a good solution to the NCP. A potential advantage of the RSGA is its scalability in complex networks, where permutation representation based GAs may face serious memory-efficiency problems. The effectiveness of the proposed RSGA is illustrated in the context of some experiments.