Electronic Notes in Discrete Mathematics最新文献

Many studies had been made on optimization problems related to the maintenance operation works in the railway world. In this paper, we focus on lesser-known type of these problems. Here, the maintenance is already scheduled and the infrastructure manager can only change the train timetables and the routing. This problem is not well treated in the literature. In this work, we define the problem and we present a model. Since several days are available to solve the problem, the level of abstraction of the model and the size of the considered instances let us use an exact method. We propose a Mixed Integer Linear Program minimizing the primary delays. Results on real world instances are reported.

We formulate and solve a mixed-integer linear program to model an agribusiness two-echelon supply chain between an agro-industrial producer and a wholesaler. The presented model is an equivalent reformulation of a bilevel linear program, using the well known KKT conditions and a disjunction approach on the complementary constraints. It includes a hierarchical decision structure that contemplates an agro-industrial producer in the upper level, who maximizes its profit by delineating the field into management zones and assigning to each one a specific crop rotation plan. In turn, in the lower level is the wholesaler who minimizes the penalization cost of lost sales that could experiment in order to satisfy the demand requirement according to the units provided by the producer. We present a case study to show the relevance of the proposed methodology.

Many combinatorial optimisation problems are NP-Hard. Yet in practice high quality solutions are often obtained by (meta)heuristics. These work well in some cases, but not in others, indicating a potential for algorithm selection. In this extended abstract is discussed how to apply algorithm selection to a combinatorial optimisation problem and which challenges arise when doing so. The generalised assignment problem is used as case study.

The impact of congestion in transportation has become one of the main concerns regarding urban planing in large cities. Time-Dependent Vehicle Routing Problems (TDVRPs) is the name given to a broad family of VRPs that explicitly incorporate the congestion by considering variable travel times. In this paper we study the Time-Dependent Elementary Shortest Path Problem with Resource Constraints (TDESPPRC), that appears as the pricing sub-problem in column generation-based approaches for TDVRPs. We consider two integer programming formulations which exploit the characteristics of the time-dependent travel time function and are evaluated on benchmark instances. On preliminary computational experiments, the approach is able to effectively solve instances with up to 25 vertices in reasonable times, showing its potential to be used within a Branch and Price algorithm.

We consider a new variant of the knapsack problem, where the contribution of each item on total profit is determined by its position in the knapsack via a specific function. While in the classic version this function could be considered a constant, we study two non-monotone convex functions motived by several real applications. We propose a binary linear programming (BLP) model and a polynomial time algorithm, called Greedy. Computational experiments are carried out, discussing practical and theoretical aspects of the problem resolution.

A novel method to model the problem of 3-coloring on outerplanar graphs is presented. The proposal is based on the specification of the logical constraints for the 3-coloring of an outerplanar graph in a dinaymic way, resulting in a polynomial-time instance of the incremental satisfiability problem. This proposal can be extended to consider other polynomial-time instances of the 3-coloring problem.

In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I show a way of modeling it as a Maximum Weighted Stable Set Problem which is further used to solve a real astronomical instance and I partially characterize the forbidden subgraphs of the resulting family of graphs given by that reduction. Finally, I prove that the problem is N P-Hard.

In this paper we present a general framework for the ex post evaluation of an operating theatre driven by different performance criteria. We tested such a framework on a real case study proposing also a comparison with the actual situation.

We introduce a new line of analysis of Flow Shop scheduling problems, for the case of two jobs and assuming that processing times are unknown. The goal is to determine the domination relations between permutation and non-permutation schedules. We analyze the structural and dominance properties that ensue in this setting, based on the critical paths of schedules.

The article investigates different implementations of a Variable Neighborhood Search approach for the Capacitated Vehicle Routing Problem. An important goal of the work presented here is to obtain an understanding of the potential effects of implementation details on the observed performance of the algorithm.

Our work is motivated by our experiences in implementation competitions, in which best-possible algorithms to hard optimization problems must be devised and delivered. In those contexts, we may ask: what determines the success of an algorithm, (i) some key algorithmic ingredient, (ii) coding details, or (iii) other aspects? Here, we try analysing (ii) and (iii). Overall, we are able to identify some important details that are often neglected in scientific articles. Moreover, and in order to allow anyone to re-produce our findings, we make the source-code of our implementation available online with this article [Martin Josef Geiger. Different implementations of a metaheuristic for the capacitated vehicle routing problem. Mendeley Data, 2018. https://dx.doi.org/10.17632/s4h89j4tgp.2].