Firefly Algorithm, Stochastic Test Functions and Design Optimisation

Modern optimisation algorithms are often metaheuristic, and they are very promising in solving NP-hard optimization problems. In this paper, we show how to use the recently developed Firefly Algorithm to solve nonlinear design problems. For the standard pressure vessel design optimisation, the optimal solution found by FA is far better than the best solution obtained previously in literature. In addition, we also propose a few new test functions with either singularity or stochastic components but with known global optimality, and thus they can be used to validate new optimisation algorithms. Possible topics for further research are also discussed.Comment: 12 pages, 11 figure

Moduli space of logarithmic states in critical massive gravities

We take new algebraic and geometric perspectives on the combinatorial results recently obtained on the partition functions of critical massive gravities conjectured to be dual to Logarithmic CFTs throught the AdS$_3$/LCFT$_2$ correspondence. We show that the partition functions of logarithmic states can be expressed in terms of Schur polynomials. Subsequently, we show that the moduli space of the logarithmic states is the symmetric product $S^n \left( \mathbb{C}^2 \right)$. As the quotient of an affine space by the symmetric group, this orbifold space is shown to be described by Hilbert series that have palindromic numerators. The palindromic properties of the Hilbert series indicate that the orbifolds are Calabi-Yau, and allow for a new interpretation of the logarithmic state spaces in critical massive gravities as Calabi-Yau singular spaces.Comment: 35 pages, v2: major revision, modified title, added references, stronger conclusion

The twisted Wilson fermion for the Standard Model on a lattice

We present a preliminary study of a chiral-gauge-invariant Wilson term for the Standard Model on a lattice. In the strong coupling limit for doublers, this Wilson term shows that the doublers of leptons (quarks) are anti-baryons (anti-leptoquarks), and they are decoupled by getting gauge invariant masses. We discuss that the possibility of achieving the low-energy Standard Model could be realized by the ``three-fermion-cuts'' at the weak coupling limit for normal modes, where baryons and leptoquarks dissolve into their constituents.Comment: 3 pages LaTex espcrc2.sty, Lat97 (chiral fermions) Edinburg

Free Lunch or No Free Lunch: That is not Just a Question?

The increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important studies on convergence analysis of various metaheuristic algorithms have proven to be fruitful. This paper discusses the recent results on no-free-lunch theorems and algorithm convergence, as well as their important implications for algorithm development in practice. Free lunches may exist for certain types of problem. In addition, we will highlight some open problems for further research.Comment: 14 page