'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126

Bayesian Optimisation Algorithm for Nurse Scheduling, Scalable Optimization via Probabilistic Modeling

Our research has shown that schedules can be built mimicking a human scheduler by using a set of rules that involve domain knowledge. This chapter presents a Bayesian Optimization Algorithm (BOA) for the nurse scheduling problem that chooses such suitable scheduling rules from a set for each nurse’s assignment. Based on the idea of using probabilistic models, the BOA builds a Bayesian network for the set of promising solutions and samples these networks to generate new candidate solutions. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed algorithm may be suitable for other scheduling problems

A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem

E-handel är i nuläget ett etablerat fenomen som växer för varje år. I samband med att e-handen breder ut sig och försäljningen mellan olika länder ökar bidrar det även till en ökad returgrad. Returgraden inom e-handel är den högsta i jämförelse med övriga försäljningskanaler och är ett hot för många företags överlevnad. För att vända returen till någonting positivt kan returprocessen användas för att stärka kundlojalitet och kundvärde genom segmenterade lösningar.  Syftet med rapporten är att identifiera de steg en konsument går igenom i en returprocess och om dessa aktiviteter kan skapa lojalitet och kundtillfredsställelse som stärker relation mellan konsument och företag. För studien utformades det en enkätundersökning för konsumenter som returnerat en produkt på Etonshirts.com. Från enkätundersökningen framgick det att stor andel av respondenterna var mycket nöjda med företagets returprocess men även att det fanns områden som kan utvecklas. För att bekräfta vilka steg en konsument går igenom under en returprocess gjordes en flerfallstudie av fem svenska e-handelsföretag. Studien bekräftar vilka steg som finns och att de kan skilja sig mellan företag. En observationsstudie utfördes i syfte med att identifiera företagets steg i en returprocess, detta för att bekräfta vilka steg ett företag har och hur det i sin tur påverkar kundens process.  För att en återförsäljare ska kunna generera kundnöjdhet måste återförsäljaren förstå sina konsumenters beteende och en returprocess bör anpassas beroende på segment och marknad. Kundnöjdheten kan nås genom effektivitet, bekvämlighet och noggrannhet som bidrar till lojala kunder. Beroende på hur företaget presenterar information på webbplatsen, om köpet, retursedel och returpolicy bidrar det till hur kunden upplever returprocessen och i vilken utsträckning en konsument returnerar. Den totala upplevelsen av köp och retur är viktig för att stärka relation mellan kund och företag.  E-commerce is an established phenomenon that grows for each year. As the e-commerce expands and sales between different countries increase, it also contributes to an increased return rate. The return of e-commerce is the highest in comparison with other sales channels and is a threat to many online companies. In order to turn the return into something positive, the return process can be used to strengthen customer loyalty and customer value through segmented solutions. The purpose of this report is to chart the activities a consumer goes through in a return process and investigate if these activities can create loyalty and customer satisfaction that strengthen consumer / business relationship. For the study, a survey was conducted for consumers who returned a product on Etonshirts.com. From the survey, it was found that a large proportion of respondents were very pleased with the company's return process, but also that there were areas that could be developed. To confirm what activities a consumer is going through during a return process, a multivariate study was conducted at five Swedish ecommerce companies. The study confirms which steps exist and that they can differ between companies. An observation study was conducted to map the company's steps in a return process, to confirm what activities a company has and how it affects the customers return process. In order for a company to generate customer satisfaction, they must understand the behaviour of their consumers and a return process should be customized depending on segment and market. Customer satisfaction can be achieved through efficiency, convenience and accuracy that contribute to loyal customers. Depending on how the company presents information on the website, the purchase, return and return policy, it helps to understand how the customer experiences the return process and to which extent a consumer returns. The overall experience of purchase and returns is important in strengthening relationships between customers and companies. 

A Bayesian optimization algorithm for the nurse scheduling problem

A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse’s assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems

The Application of Bayesian Optimization and Classifier Systems in Nurse Scheduling

Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each persons assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems

'The application of Bayesian Optimization and Classifier Systems in Nurse Scheduling'

Abstract. Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person's assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems

A Literature Review of Cuckoo Search Algorithm

Optimization techniques play key role in real world problems. In many situations where decisions are taken based on random search they are used. But choosing optimal Optimization algorithm is a major challenge to the user. This paper presents a review on Cuckoo Search Algorithm which can replace many traditionally used techniques. Cuckoo search uses Levi flight strategy based on Egg laying Radius in deriving the solution specific to problem. CS optimization algorithm increases the efficiency, accuracy, and convergence rate. Different categories of the cuckoo search and several applications of the cuckoo search are reviewed. Keywords: Cuckoo Search Optimization, Applications , Levy Flight DOI: 10.7176/JEP/11-8-01 Publication date:March 31st 202