Beam search is a fast and empirically effective method for translation decoding, but it lacks formal guarantees about search error. We develop a new decoding algorithm that combines the speed of beam search with the optimal certificate property of Lagrangian relaxation, and apply it to phraseand syntax-based translation decoding. The new method is efficient, utilizes standard MT algorithms, and...

In this paper an application of a combined method for the profit based unit commitment problem (PBUC) using Genetic Algorithm and Lagrangian Relaxation (LR) is presented. The algorithm is proposed to solve PBUC under deregulated environment with the objective of maximizing GENCO’s profit and minimizing the operating cost. The problem formulation of the unit commitment takes into consideration t...

This paper is devoted to the numerical resolution of unit-commitment problems, with emphasis on the French model optimizing the daily production of electricity. The solution process has two phases. First a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. We then propose to use the latter in the second phase, for a heuristic resolution based o...

We formulate and solve a discrete-time path-optimization problem where a single searcher, operating in a discretized 3-dimensional airspace, looks for a moving target in a finite set of cells. The searcher is constrained by maximum limits on the consumption of several resources such as time, fuel, and risk along any path. We develop a specialized branch-and-bound algorithm for this problem that...

We present a direct analytical algorithm for solving transportation problems with quadratic function cost coefficients. The algorithm uses the concept of absolute points developed by the authors in earlier works. The versatility of the proposed algorithm is evidenced by the fact that quadratic functions are often used as approximations for other functions, as in, for example, regression analysi...

The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be obtained using Linear Programming formulations, but these are computationally expensive for large...

We present a fully polynomial-time approximation scheme for a multicommodity flow problem that yields lower bounds of the graph bisection problem. We compare the approximation algorithm with Lagrangian relaxation based cost-decomposition approaches and linear programming software when embedded in an exact branch&bound approach for graph bisection. It is shown that the approximation algorithm is...

This paper focuses on a production scheduling problem in a tree-structured assembly system operating on a make-toorder basis. Due dates are considered as constraints in the problem, that is, tardiness is not allowed. The objective of the problem is to minimize holding costs of ®nal product inventory as well as work-in-process inventory. A mixed integer linear programming model is given and a br...