This paper presents a multi-objective Particle Swarm Optimization (PSO) algorithm for worker assignment and mixed-model assembly line balancing problem when task times depend on the worker’s skill level. The objectives of this model are minimization of the number of stations (equivalent to the maximization of the weighted line efficiency), minimization of the weighted smoothness index and minim...

1.1 Projective spaces and spreads. A projective space is a geometry consisting of a set of points and a set of lines, where each line is a subset of the point set, such that the following axioms hold: • Any two points are on exactly one line. • Let A, B, C, D be four distinct points no three of which are collinear. If the lines AB and CD intersect each other, then the lines AD and BC also inter...

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative ...

We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. We show how to express this as a reductive quotient and so a GIT problem, thus defining a notion of stability for orbifolds. We then prove an...

We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing a result of Jaffe-Taubes [19] for the action of the circle on the complex line. Namely, suppose a compact connected Lie group K acts on a Kähler manifold X with proper moment map so that stable=semistable for the action of the complexified Lie group G and X is equivariantly convex at infinity. Then, for some sufficient...

In an earlier paper we explained how to convert the problem of symplectically embedding one 4-dimensional ellipsoid into another into the problem of embedding a certain set of disjoint balls into CP 2 by using a new way to desingularize orbifold blow ups Z of the weighted projective space CP 2 1,m,n. We now use a related method to construct symplectomorphisms of these spaces Z. This allows us t...