A4A_4 Group and Tri-bimaximal Neutrino Mixing -- A Renormalizable Model

The tetrahedron $A_4$ group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, $\chi$ and $\chi'$, transforming under $A_4$ as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating $\chi$ and $\chi'$ from communicating with each other. The clash of the different vev structures for $\chi$ and $\chi'$ is the so called sequestering problem. In this work, I show that it is possible to construct renormalizable supersymmetric models producing the tri-bimaximal neutrino mixing with no sequestering problem.Comment: 4 page

A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm