arXiv subjects

Elif Radová Garajová

Publications and source records attributed to Elif Radová Garajová.

2 recordsLinked to original sources

arXiv2026

Heuristics for the Worst Optimal Value of Interval Transportation Problems

An interval transportation problem represents a model for a transportation problem in which the values of supply, demand, and transportation costs are affected by uncertainty and can vary independently within given interval ranges. One of the main tasks of solving interval programming models is computing the best and worst optimal value over all possible choices of the interval data. Although the best optimal value of an interval transportation problem can be computed in polynomial time, computing the worst (finite) optimal value was proved to be NP-hard. In this paper, we strengthen a previous result showing a quasi-extreme decomposition for finding the worst optimal value, and building on the result, we design heuristics for efficiently approximating the value. Using a simplified encoding of the scenarios, we first derive a local search method and a genetic algorithm for approximating the worst optimal value. Then, we integrate the two methods into a memetic algorithm, which combines the evolutionary improvement of a genetic algorithm with individual learning implemented via local search. Moreover, we include numerical experiments for a practical comparison of the three different approaches. We also show that the proposed memetic algorithm is competitive with the available state-of-the-art methods for approximating the worst optimal value of interval transportation problems, this is demonstrated by finding the new best solutions for several instances, among others.

math.OC↗

arXiv2026

Minimum cost network flow with interval capacities: The worst-case scenario

We study the problem of determining the worst optimal value and characterizing the corresponding worst-case scenarios in minimum cost network flow problems with interval uncertainty in arc capacities. In this setting, each capacity can take any value within its specified lower and upper bounds. We prove that computing the worst optimal value is a strongly NP-hard problem and remains NP-hard even when restricted to series-parallel graphs. Further, we propose a mixed-integer linear programming formulation that computes the exact worst optimal value, as well as a pseudopolynomial-time algorithm designed for the special case of series-parallel graphs. We also examine the structural properties of the most extremal worst-case scenarios and show that the arcs whose capacities are not fixed at their interval bounds form a forest. This result establishes an upper bound on the number of such arcs, which we show to be tight by constructing a class of instances in which the bound is attained. Finally, we investigate the more-for-less paradox in minimum cost network flow problems with interval capacities, which occurs in instances where increasing the required flow leads to a decrease in the worst-case optimal cost. We provide a general characterization of this phenomenon using augmenting paths and establish a stronger characterization for complete graphs. In addition, we discuss the properties of the cost matrices immune against the paradox and prove that deciding whether a given cost matrix has this property is a strongly co-NP-hard problem.

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