The two-machine flow shop sequencing problem with arbitrary release dates of jobs and the minimum makespan criterion is considered. The problem is known to be NP-hard, and the best known approximation algorithms are those of Potts (1985) with a worst-case performance ratio of 5/3 and running time $O(n^3 \log n)$, and a polynomial time approximation … Read more
Geometric optimization is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the well-known associated duality theory, using conic optimization. After introducing suitable convex cones and studying their properties, we model geometric optimization problems with a conic formulation, which allows us to … Read more
Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to … Read more
This paper describes variants of GRASP (greedy randomized adaptive search procedure) with path relinking for the three index assignment problem (AP3). GRASP is a multi-start metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path relinking is an intensification strategy that explores … Read more
For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. … Read more
A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. … Read more
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets. For the … Read more
We consider the multi-stage multiprocessor flowshop scheduling problem with uniform machines at each stage and the minimum makespan objective. Using a vector summation technique, three polynomial-time heuristics are developed with absolute worst-case performance guarantees. As a direct corollary, in the special case of the ordinary flowshop problem we come to the best approximation algorithms (both … Read more
Networks 39 (2002), 216-231. CitationNetworks 39 (2002), 216-231.
A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more