Solving Sudoku with Ant Colony Optimization

In this paper we present a new algorithm for the well-known and computationally-challenging Sudoku puzzle game. Our Ant Colony Optimization-based method significantly out-performs the state-of-the-art algorithm on the hardest, large instances of Sudoku. We provide evidence that – compared to traditional backtracking methods – our algorithm offers a much more efficient search of the solution space, and demonstrate the utility of a novel anti-stagnation operator. This work lays the foundation for future work on a general-purpose puzzle solver, and establishes Japanese pencil puzzles as a suitable platform for benchmarking a wide range of algorithms

Equity Premium and Consumption Sensitivity When the Consumer- Investor Allows for Unfavorable Circumstances

Introducing one additional element due to possible misfortune to the return of each of two assets in the basic model of Samuelson (Rev.Econom.Statist.51 (1969)239)on optimum portfolio and consumption decisions,this paper resolves both the excess equity premium and the excess consumption sensitivity puzzles.This uni ed treatment provides a framework to study how important state variables will a ect the change in aggregate consumption which is consid- ered unpredictable in one formulation of the permanent income hypothesis.The implications of the theory agree with empirical results reported here and elsewhere.The theoretical framework appears to be simple and powerful as compared with alternative theories to explain the two puzzles.Optimum consumption and investment;Asset pricing;Consumption sensitivity;Robust control; The Lagrange method

Long Dated Life Insurance and Pension Contracts

We discuss the "life cycle model" by first introducing a credit market with only biometric risk, and then market risk is introduced via risky securities. This framework enables us to find optimal pension plans and life insurance contracts where the benefits are state dependent. We compare these solutions both to the ones of standard actuarial theory, and to policies offered in practice. Two related portfolio choice puzzles are discussed in the light of recent research, one is the horizon problem, the other is related to the aggregate market data of the last century, where theory and practice diverge. Finally we present some comments on longevity risk and cohort risk.The life cycle model; pension insurance; optimal life insurance; longevity risk; the horizon problem; equity premium puzzle

Applications of Nonlinear Optimization

We apply an interior point algorithm to two nonlinear optimization problems and achieve improved results. We also devise an approximate convex functional alternative for use in one of the problems and estimate its accuracy. The first problem is maximum variance unfolding in machine learning. The traditional method to solve this problem is to convert it to a semi-definite optimization problem by defining a kernel matrix. We obtain better unfolding and higher speeds with the interior point algorithm on the original non-convex problem for data with less than 10,000 points. The second problem is a multi-objective dose optimization for intensity modulated radiotherapy, whose goals are to achieve high radiation dose on tumors while sparing normal tissues. Due to tumor motions and patient set-up errors, a robust optimization against motion uncertainties is required to deliver a clinically acceptable treatment plan. The traditional method, to irradiate an enlargement of the tumor region, is very conservative and leads to possibly high radiation dose on sensitive structures. We use a new robust optimization model within the framework of goal programming that consists of multiple optimization steps based on prescription priorities. One metric is defined for each structure of interest. A final robustness optimization step then minimizes the variance of all the goal metrics with respect to the motion probability space, and pushes the mean values of these metrics toward a desired value as well. We show similar high dose coverage on example tumors with reduced dose on sensitive structures. One clinically important metric for a radiation dose distribution, that describes tumor control probability or normal tissue complication probability, is Dx, the minimum dose value on the hottest x% of a structure. It is not mathematically well-behaved, which impedes its use in optimization. We approximate Dx with a linear function of two generalized equivalent uniform dose metrics, also known as lp norms, requiring that the approximation is concave so that its maximization becomes a convex problem. Results with cross validation on a sampling of radiation therapy plans show that the error of this approximation is less than 1 Gy for the most used range 80 to 95 of x values

Extensible Automated Constraint Modelling

In constraint solving, a critical bottleneck is the formulationof an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature