E-BLOW: E-Beam Lithography Overlapping aware Stencil Planning for MCC System

Electron beam lithography (EBL) is a promising maskless solution for the technology beyond 14nm logic node. To overcome its throughput limitation, recently the traditional EBL system is extended into MCC system. %to further improve the throughput. In this paper, we present E-BLOW, a tool to solve the overlapping aware stencil planning (OSP) problems in MCC system. E-BLOW is integrated with several novel speedup techniques, i.e., successive relaxation, dynamic programming and KD-Tree based clustering, to achieve a good performance in terms of runtime and solution quality. Experimental results show that, compared with previous works, E-BLOW demonstrates better performance for both conventional EBL system and MCC system

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

The Guided Improvement Algorithm for Exact, General-Purpose, Many-Objective Combinatorial Optimization

This paper presents a new general-purpose algorithm for exact solving of combinatorial many-objective optimization problems. We call this new algorithm the guided improvement algorithm. The algorithm is implemented on top of the non-optimizing relational constraint solver Kodkod. We compare the performance of this new algorithm against two algorithms from the literature [Gavanelli 2002, Lukasiewycz et alia 2007, Laumanns et alia 2006]) on three micro-benchmark problems (n-Queens, n-Rooks, and knapsack) and on two aerospace case studies. Results indicate that the new algorithm is better for the kinds of many-objective problems that our aerospace collaborators are interested in solving. The new algorithm returns Pareto-optimal solutions as it computes

Exact algorithms for the 0–1 Time-Bomb Knapsack Problem

We consider a stochastic version of the 0–1 Knapsack Problem in which, in addition to profit and weight, each item is associated with a probability of exploding and destroying all the contents of the knapsack. The objective is to maximise the expected profit of the selected items. The resulting problem, denoted as 0–1 Time-Bomb Knapsack Problem (01-TB-KP), has applications in logistics and cloud computing scheduling. We introduce a nonlinear mathematical formulation of the problem, study its computational complexity, and propose techniques to derive upper and lower bounds using convex optimisation and integer linear programming. We present three exact approaches based on enumeration, branch and bound, and dynamic programming, and computationally evaluate their performance on a large set of benchmark instances. The computational analysis shows that the proposed methods outperform the direct application of nonlinear solvers on the mathematical model, and provide high quality solutions in a limited amount of time