arXiv subjects

Felix Engelhardt

Publications and source records attributed to Felix Engelhardt.

6 recordsLinked to original sources

arXiv2025

Counterfactual Explanations for Integer Optimization Problems

Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization models, CEs have primarily been studied in limited contexts and little research has been done on CEs for general integer optimization problems. In this work, we address this gap. We first show that the general problem of constructing a CE is $\Sigma_2^p$-complete even for binary integer programs with just a single mutable constraint. Second, we propose solution algorithms for several of the most tractable special cases: (i) mutable objective parameters, (ii) a single mutable constraint, (iii) mutable right-hand-side, and (iv) all input parameters can be modified. We evaluate our approach using classical knapsack problem instances, focusing on cases with mutable constraint parameters. Additionally, we present experiments on the resource constrained shortest path problem.

math.OC↗

arXiv2025

Minimum-Peak-Cost Flows Over Time

When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver parcels with a single truck over eight hours than to use two trucks for four hours, as long as the time suffices. To model such scenarios, we introduce the novel minimum peak cost flow over time problem, whose objective is to minimise the maximum cost at all points in time rather than minimising the integral of costs. We focus on minimising peak costs of temporally repeated flows. These are desirable for practical applications due to their simple structure. This yields the minimum-peak-cost temporally repeated flow problem (MPC-TRF). We show that the simple structure of temporally repeated flows comes with the drawback of arbitrarily bad approximation ratios compared to general flows over time. Furthermore, our complexity analysis shows the integral version of MPC-TRF is strongly NP-hard, even under strong restrictions. On the positive side, we identify two benign special cases: unit-cost series-parallel networks and networks with time horizon at least twice as long as the longest path in the network (with respect to the transit time). In both cases, we show that integral optimal flows if the desired flow value equals the maximum flow value and fractional optimal flows for arbitrary flow values can be found in polynomial time. For each of these cases, we provide an explicit algorithm that constructs an optimal solution.

cs.DS↗

arXiv2025

Robust Capacity Expansion Modelling for Renewable Energy Systems

Future greenhouse gas neutral energy systems will be dominated by renewable energy technologies providing variable supply subject to uncertain weather conditions. For this setting, we propose an algorithm for capacity expansion planning: We evaluate solutions optimised on a single years' data under different input weather years, and iteratively modify solutions whenever supply gaps are detected. These modifications lead to solutions with sufficient capacities to overcome periods of cold dark lulls and seasonal demand/supply fluctuations. A computational study on a German energy system model for 40 operating years shows that preventing supply gaps, i.e. finding a robust system, increases the total annual cost by 1.6-2.9%. In comparison, non-robust systems display loss of load close to 50% of total demand during some periods. Results underline the importance of assessing the feasibility of energy system models using atypical time-series, combining dark lull and cold period effects.

math.OC↗

arXiv2025

Combinatorial and Computational Insights about Patient-to-room Assignment under Consideration of Roommate Compatibility

During a hospital stay, a roommate can significantly influence a patient's overall experience both positivly and negatively. Therefore, hospital staff tries to assign patients together to a room that are likely to be compatible. However, there are more conditions and objectives to be respected by the patient-to-room assignment (PRA), e.g., ensuring gender separated rooms and avoiding transfers. In this paper, we review the literature for reasons why roommate compatibility is important as well as for criteria that can help to increase the probability that two patients are suitable roommates. We further present combinatorial insights about computing patient-to-room assignments with optimal overall roommate compatibility. We then compare different IP-formulations for PRA as well as the influence of different scoring functions for patient compatibility on the runtime of PRA integer programming (IP) optimisation. Using these results and real-world data, we conclude this paper by developing and evaluating a fast IP-based solution approach for the dynamic PRA.

math.OC↗

arXiv2024

Rescue Craft Allocation in Tidal Waters of the North and Baltic Sea

This paper aims to improve the average response time for naval accidents in the North and Baltic Sea. To do this we optimize the strategic distribution of the vessel fleet used by the Deutsche Gesellschaft zur Rettung Schiffbr\"uchiger (German Maritime Search and Rescue Service) (DGzRS) across several home stations. Based on these locations, in case of an incoming distress call the vessel with the lowest response time is dispatched. A particularity of the region considered is the fact that due to low tide, at predictable times some vessels and stations are not operational. In our work, we build a corresponding mathematical model for the allocation of rescue crafts to multiple stations. Thereafter, we show that the problem is NP-hard. Next, we provide an Integer Programming (IP) formulation. Finally, we propose several methods of simplifying the model and do a case study to compare their effectiveness. For this, we generate test instances based on real-world data.

math.OC↗

arXiv2023

Structural Insights and an IP-based Solution Method for Patient-to-room Assignment under Consideration of Single Room Entitlements

Patient-to-room assignment (PRA) is a scheduling problem in decision support for hospitals. It consists of assigning patients to rooms according to certain objectives, e.g., avoiding transfers and respecting single-room requests. This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms. We further compare different IP-formulations for PRA as well as the influence of different objectivs on the runtime. Based on these results, we develop a fast IP-based solution approach which obtains high quality solution. The applicability is verified through a computational study with instances derived from real-world data. Results indicate that large, real world instances can be solved to a high degree of optimality within (fractions of) seconds.

math.OC↗