An electromagnetic meta-heuristic for the nurse scheduling problem

In this paper, we present a novel meta-heuristic technique for the nurse scheduling problem (NSP). This well-known scheduling problem assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The problem is known to be NP-hard. Due to its complexity and relevance, many algorithms have been developed to solve practical and often case-specific models of the NSP. The huge variety of constraints and the several objective function possibilities have led to exact and meta-heuristic procedures in various guises, and hence comparison and state-of-the-art reporting of standard results seem to be a utopian idea. We present a meta-heuristic procedure for the NSP based on the framework proposed by Birbil and Fang (J. Glob. Opt. 25, 263–282, 2003). The Electromagnetic (EM) approach is based on the theory of physics, and simulates attraction and repulsion of sample points in order to move towards a promising solution. Moreover, we present computational experiments on a standard benchmark dataset, and solve problem instances under different assumptions. We show that the proposed procedure performs consistently well under many different circumstances, and hence, can be considered as robust against case-specific constraints.     

Extending a class of continuous estimation of distribution algorithms to dynamic problems

In this paper, a class of continuous Estimation of Distribution Algorithms (EDAs) based on Gaussian models is analyzed to investigate their potential for solving dynamic optimization problems where the global optima may change dramatically during time. Experimental results on a number of dynamic problems show that the proposed strategy for dynamic optimization can significantly improve the performance of the original EDAs and the optimal solutions can be consistently located.     

Comparison and hybridization of crossover operators for the nurse scheduling problem

In this paper, we present a hybrid genetic algorithm for the well-known nurse scheduling problem (NSP). The NSP involves the construction of roster schedules for nursing staff in order to maximize the quality of the roster schedule subject to various hard constraints. In the literature, several genetic algorithms have been proposed to solve the NSP under various assumptions. The contribution of this paper is twofold. First, we extensively compare the various crossover operators and test them on a standard dataset in a solitary approach. Second, we propose several options to hybridize the various crossover operators.     

On the characterization and generation of nurse scheduling problem instances

Due to its complexity and relevance in practice, many different procedures have been proposed in the operations research literature to solve the well-known nurse scheduling problem (NSP). The NSP assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The often highly case-specific workplace conditions in hospital departments have resulted in the development of dedicated (meta-)heuristics to find a workable schedule in an acceptable time limit. However, in spite of research community posing a growing need for benchmarking, these procedures lack any base for comparison.     

Optimizing logistic regression coefficients for discrimination and calibration using estimation of distribution algorithms

Logistic regression is a simple and efficient supervised learning algorithm for estimating the probability of an outcome or class variable. In spite of its simplicity, logistic regression has shown very good performance in a range of fields. It is widely accepted in a range of fields because its results are easy to interpret. Fitting the logistic regression model usually involves using the principle of maximum likelihood. The Newton–Raphson algorithm is the most common numerical approach for obtaining the coefficients maximizing the likelihood of the data. This work presents a novel approach for fitting the logistic regression model based on estimation of distribution algorithms (EDAs), a tool for evolutionary computation. EDAs are suitable not only for maximizing the likelihood, but also for maximizing the area under the receiver operating characteristic curve (AUC). Thus, we tackle the logistic regression problem from a double perspective: likelihood-based to calibrate the model and AUC-based to discriminate between the different classes. Under these two objectives of calibration and discrimination, the Pareto front can be obtained in our EDA framework. These fronts are compared with those yielded by a multiobjective EDA recently introduced in the literature.      

Solving the multi-objective nurse scheduling problem with a weighted cost function

The primary objective of the nurse scheduling problem is to ensure there are sufficient nurses on each shift. There are also a number of secondary objectives designed to make the schedule more pleasant. Neighbourhood search implementations use a weighted cost function with the weights dependent on the importance of each objective. Setting the weights on binding constraints so they are satisfied but still allow the search to find good solutions is difficult. This paper compares two methods for overcoming this problem, SAWing and Noising with simulated annealing and demonstrates that Noising produces better schedules.     

An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times

The paper deals with the m-machine permutation flow shop scheduling problem in which job processing times, along with a processing order, are decision variables. It is assumed that the cost of processing a job on each machine is a linear function of its processing time and the overall schedule cost to be minimized is the total processing cost plus maximum completion time cost. A algorithm for the problem with m = 2 is provided; the best approximation algorithm until now has a worst-case performance ratio equal to . An extension to the m-machine (m ≥2) permutation flow shop problem yields an approximation algorithm with a worst-case bound equal to

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, where is the worst-case performance ratio of a procedure used, in the proposed algorithm, for solving the (pure) sequencing problem. Moreover, examples which achieve this bound for = 1 are also presented.     

A linear time algorithm for restricted bin packing and scheduling problems

In this paper we are concerned with the subproblem of bin packing, where the set of possible weights of elements is finite. In [5] it was mentioned that this problem could be solved by an exhaustive search procedure in polynomial time, but the degree of the polynomial is high and increases as the cardinality of the set of weights increases. However, we will show that a more careful analysis of the problem leads to a linear time algorithm. The impact of this result on task scheduling is discussed.     

Solving a bi-objective nurse rerostering problem by using a utopic Pareto genetic heuristic

Nurse rerostering arises when at least one nurse announces that she will be unable to undertake the tasks previously assigned to her. The problem amounts to building a new roster that satisfies the hard constraints already met by the current one and, as much as possible, fulfils two groups of soft constraints which define the two objectives to be attained. A bi-objective genetic heuristic was designed on the basis of a population of individuals characterised by pairs of chromosomes, whose fitness complies with the Pareto ranking of the respective decoded solution. It includes an elitist policy, as well as a new utopic strategy, introduced for purposes of diversification. The computational experiments produced promising results for the practical application of this approach to real life instances arising from a public hospital in Lisbon.     

堆取料机调度问题的一个近似算法

研究源自煤炭港口料场管理的堆取料机调度问题.该问题中,堆取料机从长为L的料场作业区最左端开始空机或载料运行,两者的速度之比为s：1（s ≥ 1）.决策者需确定储料堆在作业区的分布以及堆取料机处理它们的先后次序,目的是极小化一批煤料运输船的在港服务时间.考虑堆取料机处理完毕需要回到料场终端的作业模型,证明了存在最坏情况界不超过1+1/4s的近似算法.     

A hybrid genetic algorithm for the repetition free longest common subsequence problem

Computing the longest common subsequence of two sequences is one of the most studied algorithmic problems. In this work we focus on a particular variant of the problem, called repetition free longest common subsequence (RF-LCS$\text{<small-caps>RF-LCS</small-caps>}$), which has been proved to be NP-hard. We propose a hybrid genetic algorithm, which combines standard genetic algorithms and estimation of distribution algorithms, to solve this problem. An experimental comparison with some well-known approximation algorithms shows the suitability of the proposed technique.     

An estimation of distribution algorithm with intelligent local search for rule-based nurse rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, that is, we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, that is, an estimation of the probability distribution of individual nurse–rule pairs that are used to construct schedules. The local search processor (ie the ant-miner) reinforces nurse–rule pairs that receive higher rewards. A challenging real-world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.     

On the convergence of a factorized distribution algorithm with truncation selection

We investigate the global convergence of a factorized distribution algorithm (FDA) with truncation selection. Like conventional genetic algorithms, FDAs maintain and successively improve a population of solutions. In FDAs, a distribution model is built based on the statistical information extracted from a set of selected solutions in the current population, and then the model thus built is used to generate new solutions for the next generation. The variable‐dependence structure of the distribution model in FDAs is determined by the variable‐interaction structure of the objective function. We prove that the FDA with truncation selection converges globally for optimization of a class of additively decomposable functions (ADF). Our results imply that the utilization of appropriately selected dependence relationships is sufficient to guarantee the global convergence of estimation of distribution algorithms (EDAs) for optimization of ADFs. © 2004 Wiley Periodicals, Inc. Complexity 9: 17–23, 2004     

A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean case

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O(m⁵logm).     

An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling

Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We develop an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of stochastic hydroelectric scheduling problems.     

A genetic algorithm for resource investment project scheduling problem,tardiness permitted with penalty

In this paper a genetic algorithm for solving a class of project scheduling problems, called Resource Investment Problem, is presented. Tardiness of project is permitted with defined penalty. Elements of algorithm such as chromosome structure, unfitness function, crossover, mutation, immigration and local search operations are explained.     

Multi-objective genetic algorithm for single machine scheduling problem under fuzziness

This paper presents a new multi-objective approach to a single machine scheduling problem in the presence of uncertainty. The uncertain parameters under consideration are due dates of jobs. They are modelled by fuzzy sets where membership degrees represent decision maker’s satisfaction grade with respect to the jobs’ completion times. The two objectives defined are to minimise the maximum and the average tardiness of the jobs. Due to fuzziness in the due dates, the two objectives become fuzzy too. In order to find a job schedule that maximises the aggregated satisfaction grade of the objectives, a hybrid algorithm that combines a multi-objective genetic algorithm with local search is developed. The algorithm is applied to solve a real-life problem of a manufacturing pottery company.     

An estimation of distribution algorithm for scheduling problem of flexible manufacturing systems using Petri nets

Based on the place-timed Petri net models of flexible manufacturing systems (FMSs), this paper proposes a novel effective estimation of distribution algorithm (EDA) for solving the scheduling problem of FMSs. A candidate solution is represented as an individual with two sections: the first contains the route information while the second is a permutation with repetition for parts. The feasibility of individuals is checked and guaranteed by a highly permissiveness deadlock controller. A feasible individual is interpreted into a deadlock-free schedule while the infeasible ones are amended. The probabilistic model in EDA is constructed via a voting procedure. An offspring individual is then produced based on the model from a seed individual, and the set of seed individuals is extracted by a roulette method from the current population. The longest common subsequence is also embedded into the probabilistic model for mining good genes. A modified variable neighborhood search is applied on offspring individuals to obtain better solutions in their neighbors and hence to improve EDA’s performance. Computational results show that our proposed algorithm outperforms all the existing ones on benchmark examples for the studied problem. It is of important practice significance for the manufacturing of time-critical and multi-type products.     

A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times

Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. This work treats a special case of the 2-cyclic robot scheduling problem when the robot route is given and the operation durations are to be chosen from prescribed intervals. The problem was previously proved to be polynomially solvable in O(m⁸log m) time. This paper proposes an improved algorithm with reduced complexity O(m⁴).     

A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem

This paper presents a genetic algorithm for solving the resource-constrained project scheduling problem. The innovative component of the algorithm is the use of a magnet-based crossover operator that can preserve up to two contiguous parts from the receiver and one contiguous part from the donator genotype. For this purpose, a number of genes in the receiver genotype absorb one another to have the same order and contiguity they have in the donator genotype. The ability of maintaining up to three contiguous parts from two parents distinguishes this crossover operator from the powerful and famous two-point crossover operator, which can maintain only two contiguous parts, both from the same parent. Comparing the performance of the new procedure with that of other procedures indicates its effectiveness and competence.