The small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)] has attracted much interests in studying the interesting properties of the networks without time-delay. However, a signal or influence travelling on the small-world networks often associated with time-delay features which are very common in biological and physical networks. We develop an analytical approach as well as numerical simulations to try to characterize the effect of time-delay on the properties of small-world networks. An analytical expression of the fractal dimension of the small-world networks is given and thus compared with the results from numerical simulations. Analysis shows that small-world networks with time-delay generally have the multifractals property.
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Cuckoo search (CS) is one of the latest nature-inspired metaheuristic algorithms, developed in 2009 by Xin-She Yang of Cambridge University and Suash Deb of C. V. Raman College of Engineering. CS is based on the brood parasitism of some cuckoo species. In addition, this algorithm is enhanced by the so-called Lévy flights rather than by simple isotropic random walks. Recent studies show that CS is potentially far more efficient than PSO, genetic algorithms, and other algorithms.
Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional algorithms may struggle to deal with such problems. A current trend is to use nature-inspired algorithms due to their flexibility and effectiveness. However, there are some key issues concerning nature-inspired computation and swarm intelligence. This paper provides an in-depth review of some recent nature-inspired algorithms with the emphasis on their search mechanisms and mathematical foundations. Some challenging issues are identified and five open problems are highlighted, concerning the analysis of algorithmic convergence and stability, parameter tuning, mathematical framework, role of benchmarking and scalability. These problems are discussed with the directions for future research.
Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.
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Integration is another important part of calculus. This chapter introduces the fundamentals of integration and methods of calculating integrals.
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Many real-world applications can be modelled as complex networks, and such networks include the Internet, epidemic disease networks, transport networks, power grids, protein-folding structures and others. Network integrity and robustness are important to ensure that crucial networks are protected and undesired harmful networks can be dismantled. Network structure and integrity can be controlled by a set of key nodes, and to find the optimal combination of nodes in a network to ensure network structure and integrity can be an NP-complete problem. Despite extensive studies, existing methods have many limitations and there are still many unresolved problems. This paper presents a probabilistic approach based on neighborhood information and node importance, namely, neighborhood information-based probabilistic algorithm (NIPA). We also define a new centrality-based importance measure (IM), which combines the contribution ratios of the neighbor nodes of each target node and two-hop node information. Our proposed NIPA has been tested for different network benchmarks and compared with three other methods: optimal attack strategy (OAS), high betweenness first (HBF) and high degree first (HDF). Experiments suggest that the proposed NIPA is most effective among all four methods. In general, NIPA can identify the most crucial node combination with higher effectiveness, and the set of optimal key nodes found by our proposed NIPA is much smaller than that by heuristic centrality prediction. In addition, many previously neglected weakly connected nodes are identified, which become a crucial part of the newly identified optimal nodes. Thus, revised strategies for protection are recommended to ensure the safeguard of network integrity. Further key issues and future research topics are also discussed.
A real-world newspaper distribution problem with recycling policy is tackled in this work. To meet all the complex restrictions contained in such a problem, it has been modeled as a rich vehicle routing problem, which can be more specifically considered as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP). This is the first study of such a problem in the literature. For this reason, a benchmark composed by 15 instances has been also proposed. In the design of this benchmark, real geographical positions have been used, located in the province of Bizkaia, Spain. For the proper treatment of this AC-VRP-SPDVCFP, a discrete firefly algorithm (DFA) has been developed. This application is the first application of the firefly algorithm to any rich vehicle routing problem. To prove that the proposed DFA is a promising technique, its performance has been compared with two other well-known techniques: an evolutionary algorithm and an evolutionary simulated annealing. Our results have shown that the DFA has outperformed these two classic meta-heuristics.
The use of fiber-reinforced polymer (FRP) shear strengthening systems for the strength enhancement of existing reinforced concrete structures is discussed. An experimental and analytical research programme is under way to investigate the performance of bonded passive and unbonded prestressed FRP shear systems, and to quantify the effect of the load history on the strengthed behavior. Non-linear finite-element analysis are being developed to model the strengthed behavior. The results will provide insight into the optimum system parameters and contribute to the formulation of design guidance for advanced FRP strengthing strategies.
Meta-heuristic algorithms are often nature-inspired, and they are becoming very powerful in solving global optimisation problems. More than a dozen major meta-heuristic algorithms have been developed over the last three decades, and there exist even more variants and hybrids of meta-heuristics. This paper intends to provide an overview of nature-inspired meta-heuristic algorithms, from a brief history to their applications. We try to analyse the main components of these algorithms and how and why they work. Then, we intend to provide a unified view of meta-heuristics by proposing a generalised evolutionary walk algorithm (GEWA). Finally, we discuss some of the important open questions.
Resource allocation in an OFDMA system has been an extremely challenging optimization task. Due to the nature of the problem, this optimization problem can be NP-hard. The majority of existing methods are based on Lagrangian duality, in combination with gradient-based methods. In this paper, we apply genetic algorithm to tune the power allocated to each sub-channel in an OFDMA system. This is done by applying GA in tuning the power allocated for the m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> user in the n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> channel (p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m,n</sub> ) after solving the resource allocation problem. The first part is a binary optimization problem, whereas the latter part is a continuous optimization problem. In solving the energy-efficient resource allocation problem, the objective is to minimize the transmitted power while fulfilling the transmission rate demand per user. Our simulation results showed that the GA method can obtain global solutions with speedy convergence.
Many quantities such as velocities and forces are vectors because they have both directions and magnitudes. In fact, vectors are crucially important in many disciplines such as engineering and physics. This chapter first introduces vectors and then presents the basic vector algebra.
