No abstract is provided for this article.
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the evolving multispecies living ecosystems. Simulations show that a small perturbation or extinction event may affect many other species in the ecosystem in an avalanche manner. Both the avalanches and the extinction arising from these changes follow a power law, reflecting that the multispecies living ecosytems have the characteristics of self-organized criticality.
No abstract is provided for this article.
A new precise experiment has been carried out to investigate Saxl's effect of the electro-static potential on the period of an electrically charged pendulum. Our experiment shows no evidence for any new interactions.
Mathematical modeling uses mathematics to build proper models for physical, chemical and biological systems. Modeling has becomes an integrated part of modern science and engineering skills. This chapter uses examples to introduce the basic steps of mathematical modeling and related techniques for solving mathematical models.
Cuckoo search is a swarm-intelligence-based algorithm that is very effective for solving highly nonlinear optimization problems. In this paper, the multiobjective cuckoo search is extended so as to obtain high-quality Pareto fronts more accurately for multiobjective optimization problems with complex constraints. The proposed approach uses a combination of the cuckoo search with non-dominated sorting and archiving techniques. The performance of the proposed approach is validated by seven test problems. The convergence property and diversity as well as uniformity are compared with those of the NSGA-II. The results show that the proposed approach can find Pareto fronts with better uniformity and quicker convergence.
Swarm intelligence has becoming a powerful technique in solving design and scheduling tasks. Metaheuristic algorithms are an integrated part of this paradigm, and particle swarm optimization is often viewed as an important landmark. The outstanding performance and efficiency of swarm-based algorithms inspired many new developments, though mathematical understanding of metaheuristics remains partly a mystery. In contrast to the classic deterministic algorithms, metaheuristics such as PSO always use some form of randomness, and such randomization now employs various techniques. This paper intends to review and analyze some of the convergence and efficiency associated with metaheuristics such as firefly algorithm, random walks, and L\'evy flights. We will discuss how these techniques are used and their implications for further research.
No abstract is provided for this article.
As an introductory mathematics book for engineers, the basic requirement is a good understanding of secondary mathematics (or GCSE level mathematics). All the fundamental concepts of engineering mathematics will gradually be introduced in a self-contained style with plenty of worked examples to aid the understanding of all important concepts. This chapter reviews the fundamentals of real numbers, sets, functions and equations.
No abstract is provided for this article.
The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimisation algorithms. However, its global optimality is not clear and there has been no mathematical proof put forward. In this paper, a detailed mathematical analysis of this problem is provided that proves that 6,059.714335048436 is the global minimum. The Lagrange multiplier method is also used as an alternative proof and this method is extended to find the global optimum of a cantilever beam design problem.
No abstract is provided for this article.
The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.
