Lars Relund Nielsen

Finding the K shortest hyperpaths

The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.

Optimal replacement policies for dairy cows based on daily yield measurements

Markov decision processes (MDP) with finite state and action space have often been used to model sequential decision making over time in dairy herds. However, the length of each stage has been at least 1 mo, resulting in models that do not support decisions on a daily basis. The present paper describes the first step of developing an MDP model that can be integrated into a modern herd management system. A hierarchical MDP was formulated for the dairy cow replacement problem with stage lengths of 1 d. It can be used to assist the farmer in replacement decisions on a daily basis and is based on daily milk yield measurements that are available in modern milking systems. Bayesian updating was used to predict the performance of each cow in the herd and economic decisions were based on the prediction. Moreover, parameters in the model were estimated using data records of the specific herd under consideration. This includes herd-specific lactation curves.

Finding the K shortest hyperpaths using reoptimization

We present some reoptimization techniques for computing (shortest) hyperpath weights in a directed hypergraph. These techniques are exploited to improve the worst-case computational complexity (as well as the practical performance) of an algorithm finding the K shortest hyperpaths in acyclic hypergraphs.

An algorithm for ranking assignments using reoptimization

We consider the problem of ranking assignments according to cost in the classical linear assignment problem. An algorithm partitioning the set of possible assignments, as suggested by Murty, is presented where, for each partition, the optimal assignment is calculated using a new reoptimization technique. Its computational performance is compared with all available implementations of algorithms with the same time complexity. The results are encouraging.

Finding the K best policies in a finite-horizon Markov decision process

Abstract Directed hypergraphs represent a general modelling and algorithmic tool, which have been successfully used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic and transportation networks. However, modelling Markov decision processes using directed hypergraphs has not yet been considered. In this paper we consider finite-horizon Markov decision processes ( MDPs ) with finite state and action space and present an algorithm for finding the K best deterministic Markov policies. That is, we are interested in ranking the first K deterministic Markov policies in non-decreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finite-horizon MDP. It is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time, with respect to the input data representing the MDP, using different additive optimality criteria.

Ranking paths in stochastic time-dependent networks

In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in some particular cases an origin–destination path must be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem.

The Bicriterion Multimodal Assignment Problem: Introduction, Analysis, and Experimental Results

We consider the bicriterion multimodal assignment problem, which is a new generalization of the classical linear assignment problem. A two-phase solution method using an effective ranking scheme is presented. The algorithm is valid for generating all nondominated criterion points or an approximation. Extensive computational results are conducted on a large library of test instances to test the performance of the algorithm and to identify hard test instances. Also, test results of the algorithm applied to the bicriterion assignment problem are provided.

A hierarchical Markov decision process modeling feeding and marketing decisions of growing pigs

Feeding is the most important cost in the production of growing pigs and has a direct impact on the marketing decisions, growth and the final quality of the meat. In this paper, we address the sequential decision problem of when to change the feed-mix within a finisher pig pen and when to pick pigs for marketing. We formulate a hierarchical Markov decision process with three levels representing the decision process. The model considers decisions related to feeding and marketing and finds the optimal decision given the current state of the pen. The state of the system is based on information from on-line repeated measurements of pig weights and feeding and is updated using a Bayesian approach. Numerical examples are given to illustrate the features of the proposed optimization model.

Bicriterion Shortest Paths in Stochastic Time-Dependent Networks

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy should correspond to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered.

Markov Decision Processes to Model Livestock Systems

Livestock farming problems are often sequential in nature. For instance at a specific time instance the decision on whether to replace an animal or not is based on known information and expectation about the future. At the next decision epoch updated information is available and the decision choice is re-evaluated. As a result Markov decision processes (MDPs) have been used to model livestock decision problems over the last decades. The objective of this chapter is to review the increasing amount of papers using MDPs to model livestock farming systems and provide an overview over the recent advances within this branch of research. Moreover, theory and algorithms for solving both ordinary and hierarchical MDPs are given and possible software for solving MDPs are considered.