Robust Assignment Problem Research Articles

An efficient methodology for robust assignment problem

This paper proposes formulations and algorithms for assignment problem under natural or physical variability, from the perspective of robustness of the assignment. We formulate the robust assignment problem as a nonlinear binary programming problem. An equivalent linear binary programming formulation and a modified Hungarian approach are then proposed to achieve computational efficiency. The proposed methods are illustrated for two example problems, where the information on the problem parameters is available as their means and standard deviations.

An efficient methodology for robust assignment problem

This paper proposes formulations and algorithms for assignment problem under natural or physical variability, from the perspective of robustness of the assignment. We formulate the robust assignment problem as a nonlinear binary programming problem. An equivalent linear binary programming formulation and a modified Hungarian approach are then proposed to achieve computational efficiency. The proposed methods are illustrated for two example problems, where the information on the problem parameters is available as their means and standard deviations.

On scenario aggregation to approximate robust combinatorial optimization problems

As most robust combinatorial min–max and min–max regret problems with discrete uncertainty sets are NP-hard, research in approximation algorithm and approximability bounds has been a fruitful area of recent work. A simple and well-known approximation algorithm is the midpoint method, where one takes the average over all scenarios, and solves a problem of nominal type. Despite its simplicity, this method still gives the best-known bound on a wide range of problems, such as robust shortest path or robust assignment problems. In this paper, we present a simple extension of the midpoint method based on scenario aggregation, which improves the current best K-approximation result to an $$(\varepsilon K)$$ -approximation for any desired $$\varepsilon > 0$$ . Our method can be applied to min–max as well as min–max regret problems.

Exact and heuristic algorithms for the interval data robust assignment problem

We consider the Assignment Problem with interval data, where it is assumed that only upper and lower bounds are known for each cost coefficient. It is required to find a minmax regret assignment. The problem is known to be strongly NP-hard. We present and compare computationally several exact and heuristic methods, including Benders decomposition, using CPLEX, a variable depth neighborhood local search, and two hybrid population-based heuristics. We report results of extensive computational experiments.

On the robust assignment problem under a fixed number of cost scenarios

We investigate the complexity of the min–max assignment problem under a fixed number of scenarios. We prove that this problem is polynomial-time equivalent to the exact perfect matching problem in bipartite graphs, an infamous combinatorial optimization problem of unknown computational complexity.

Robust characteristic polynomial assignment

In this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented. An objective function consisting of two terms is proposed, penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem. The algorithm is based on semi-infinite programming theory, and the special structure of the problem is exploited to get both simpler methods and convergence proof. The way in which the uncertain parameters affect the plant coefficients is realistic, since it includes multinomial dependence. An example of application is given to illustrate the approach.