A tensor based hyper-heuristic for nurse rostering

Nurse rostering is a well-known highly constrained scheduling problem requiring assignment of shifts to nurses satisfying a variety of constraints. Exact algorithms may fail to produce high quality solutions, hence (meta)heuristics are commonly preferred as solution methods which are often designed and tuned for specific (group of) problem instances. Hyper-heuristics have emerged as general search methodologies that mix and manage a predefined set of low level heuristics while solving computationally hard problems. In this study, we describe an online learning hyper-heuristic employing a data science technique which is capable of self-improvement via tensor analysis for nurse rostering. The proposed approach is evaluated on a well-known nurse rostering benchmark consisting of a diverse collection of instances obtained from different hospitals across the world. The empirical results indicate the success of the tensor-based hyper-heuristic, improving upon the best-known solutions for four of the instances

Machine learning for improving heuristic optimisation

Heuristics, metaheuristics and hyper-heuristics are search methodologies which have been preferred by many researchers and practitioners for solving computationally hard combinatorial optimisation problems, whenever the exact methods fail to produce high quality solutions in a reasonable amount of time. In this thesis, we introduce an advanced machine learning technique, namely, tensor analysis, into the field of heuristic optimisation. We show how the relevant data should be collected in tensorial form, analysed and used during the search process. Four case studies are presented to illustrate the capability of single and multi-episode tensor analysis processing data with high and low abstraction levels for improving heuristic optimisation. A single episode tensor analysis using data at a high abstraction level is employed to improve an iterated multi-stage hyper-heuristic for cross-domain heuristic search. The empirical results across six different problem domains from a hyper-heuristic benchmark show that significant overall performance improvement is possible. A similar approach embedding a multi-episode tensor analysis is applied to the nurse rostering problem and evaluated on a benchmark of a diverse collection of instances, obtained from different hospitals across the world. The empirical results indicate the success of the tensor-based hyper-heuristic, improving upon the best-known solutions for four particular instances. Genetic algorithm is a nature inspired metaheuristic which uses a population of multiple interacting solutions during the search. Mutation is the key variation operator in a genetic algorithm and adjusts the diversity in a population throughout the evolutionary process. Often, a fixed mutation probability is used to perturb the value at each locus, representing a unique component of a given solution. A single episode tensor analysis using data with a low abstraction level is applied to an online bin packing problem, generating locus dependent mutation probabilities. The tensor approach improves the performance of a standard genetic algorithm on almost all instances, significantly. A multi-episode tensor analysis using data with a low abstraction level is embedded into multi-agent cooperative search approach. The empirical results once again show the success of the proposed approach on a benchmark of flow shop problem instances as compared to the approach which does not make use of tensor analysis. The tensor analysis can handle the data with different levels of abstraction leading to a learning approach which can be used within different types of heuristic optimisation methods based on different underlying design philosophies, indeed improving their overall performance

The General Combinatorial Optimization Problem: Towards Automated Algorithm Design

This paper defines a new combinatorial optimisation problem, namely General Combinatorial Optimisation Problem (GCOP), whose decision variables are a set of parametric algorithmic components, i.e. algorithm design decisions. The solutions of GCOP, i.e. compositions of algorithmic components, thus represent different generic search algorithms. The objective of GCOP is to find the optimal algorithmic compositions for solving the given optimisation problems. Solving the GCOP is thus equivalent to automatically designing the best algorithms for optimisation problems. Despite recent advances, the evolutionary computation and optimisation research communities are yet to embrace formal standards that underpin automated algorithm design. In this position paper, we establish GCOP as a new standard to define different search algorithms within one unified model. We demonstrate the new GCOP model to standardise various search algorithms as well as selection hyper-heuristics. A taxonomy is defined to distinguish several widely used terminologies in automated algorithm design, namely automated algorithm composition, configuration and selection. We would like to encourage a new line of exciting research directions addressing several challenging research issues including algorithm generality, algorithm reusability, and automated algorithm design

Machine learning for improving heuristic optimisation

Heuristics, metaheuristics and hyper-heuristics are search methodologies which have been preferred by many researchers and practitioners for solving computationally hard combinatorial optimisation problems, whenever the exact methods fail to produce high quality solutions in a reasonable amount of time. In this thesis, we introduce an advanced machine learning technique, namely, tensor analysis, into the field of heuristic optimisation. We show how the relevant data should be collected in tensorial form, analysed and used during the search process. Four case studies are presented to illustrate the capability of single and multi-episode tensor analysis processing data with high and low abstraction levels for improving heuristic optimisation. A single episode tensor analysis using data at a high abstraction level is employed to improve an iterated multi-stage hyper-heuristic for cross-domain heuristic search. The empirical results across six different problem domains from a hyper-heuristic benchmark show that significant overall performance improvement is possible. A similar approach embedding a multi-episode tensor analysis is applied to the nurse rostering problem and evaluated on a benchmark of a diverse collection of instances, obtained from different hospitals across the world. The empirical results indicate the success of the tensor-based hyper-heuristic, improving upon the best-known solutions for four particular instances. Genetic algorithm is a nature inspired metaheuristic which uses a population of multiple interacting solutions during the search. Mutation is the key variation operator in a genetic algorithm and adjusts the diversity in a population throughout the evolutionary process. Often, a fixed mutation probability is used to perturb the value at each locus, representing a unique component of a given solution. A single episode tensor analysis using data with a low abstraction level is applied to an online bin packing problem, generating locus dependent mutation probabilities. The tensor approach improves the performance of a standard genetic algorithm on almost all instances, significantly. A multi-episode tensor analysis using data with a low abstraction level is embedded into multi-agent cooperative search approach. The empirical results once again show the success of the proposed approach on a benchmark of flow shop problem instances as compared to the approach which does not make use of tensor analysis. The tensor analysis can handle the data with different levels of abstraction leading to a learning approach which can be used within different types of heuristic optimisation methods based on different underlying design philosophies, indeed improving their overall performance

Optimasi Penjadwalan Staf Dengan Menggunakan Algoritma Reinforcement Learning Hyper-Heuristics Studi Kasus Rumah Sakit Ibu Dan Anak Kendangsari

dihadapi oleh setiap Rumah Sakit. Untuk itu, optimasi penjadwalan staf sangat diperlukan oleh pihak Rumah Sakit untuk mendapatkan jadwal yang sesuai dengan kebutuhan dan sumber daya manusia Rumah Sakit. Sebelum melakukan penjadwalan, ada batasan-batasan yang harus dipertimbangkan seperti aturan penjadwalan dan pembagian shift pada Rumah Sakit. Hal-hal tersebut nantinya akan digolongkan menjadi dua yaitu hard constraint dan soft constraint. Pada penelitian ini membahas tentang implementasi algortima Reinforcement Learning Hyper-Heuristic untuk menyelesaikan permasalahan penjadwalan staf di Rumah Sakit Ibu dan Anak Kendangsari. Untuk mengukur tingkat optimasi dari penjadwalan akan dihitung dari nilai Jain Fairness Index (JFI) dari masing-masing unit pada rumah sakit. Unit-unit tersebut adalah unit farmasi, bayi/NICU, gizi, IGD, Kamar Operasi, dan SIM & RM. Nilai JFI berkisar antara 0 sampai 1 dan jadwal akan semakin optimal jika nilai JFI mendekati 1. Kemudian algoritma Reinforcement Learning Hyper-Heuristic akan diterapkan untuk memilih low-level heuristic yang memiliki solusi terbaik. Low-level heuristic yang digunakan pada tugas akhir ini adalah Move dan Swap. Hasil dari optimasi ini adalah berupa perbandingan nilai JFI dari jadwal eksisting rumah sakit dengan jadwal hasil optimasi. Nilai JFI unit farmasi yang awalnya bernilai 0,80 berubah menjadi 0,97, unit bayi/NICU dari 0,67 menjadi 0,96, unit gizi dari 0,90 menjadi 0,84, unit IGD dari 0,91 menjadi 0,96, unit Kamar Operasi dari 0,80 menjadi 0,98, dan unit SIM & RM dari 0,74 menjadi 1. Hasil optimasi ini diharapkan dapat memberikan manfaat terutama bagi pihak Rumah Sakit dan staf untuk mendapatkan jadwal yang paling optimal berdasarkan tingkat keadilan untuk tiap staf. ========================================================================================================= Staff scheduling is a problem that is often faced by every hospital. For that, the optimization of staff scheduling is needed by the Hospital to get a schedule that suits the needs and the availability of human resources at the Hospital. Before scheduling, there are some constraints to be considered such as scheduling rules and the distribution of shifts in the Hospital. These constraints are also will be classified into two category, namely hard constraint and soft constraint. This study discuss about the implementation of Reinforcement Learning Hyper-Heuristic algorithm to solve the staff scheduling problem at Kendangsari’s Maternity and Child Hospital. To measure the optimization level of staff scheduling, value of Jain Fairness Index (JFI) will be calculated for each division in the hospital. These divisions are pharmacy, infant/NICU, nutrition, IGD, Operation Khamer, and Registration. JFI value ranges from 0 to 1 and the schedule will be more optimal if the value of JFI close to 1. Then the Reinforcement Learning Hyper-Heuristic algorithm will be applied to choose the low-level heuristic that has the best solution. Low-level heuristic used in this final project are Move and Swap. The result of this optimization is a comparison of JFI value from the existing schedule of the hospital and the optimization schedule. The value of the JFI pharmacy division initially valued at 0.80 changed to 0.97, the infant/NICU division from 0.67 to 0.96, the nutrition division from 0.90 to 0.84, the IGD division from 0.91 to 0.96 , Operational Khamer division from 0.80 to 0.98, and Registration division from 0.74 to 1. This resultis expected to provide benefits, especially for the Hospital and staff to get the most optimal schedule based on the fairness level for each staff

Optimasi Penjadwalan Staf Rumah Sakit Dengan Menggunakan Algoritma Tabu Search Based Hyper-Heuristics (Studi Kasus: Rumah Sakit Ibu Dan Anak Kendangsari)

Penjadwalan staf rumah sakit atau dikenal sebagai staff healthcare rostering merupakan permasalahan kompleks yang harus dihadapi setiap rumah sakit. Rumah sakit harus mempertimbangkan banyak aspek seperti jumlah perawat, pembagian shift, cost, kesempatan libur atau cuti dan constraint yang lain. Karena banyak pertimbangan tersebut, penjadwalan secara manual akan menjadi sangat sulit dan tidak bisa memberikan solusi yang optimal. Maka perlu adanya suatu model matematis untuk memudahkan permasalahan penjadwalan dengan menemukan solusi yang paling optimal. Permasalahan tersebut lebih dikenal dengan istilah nurse rostering problem (NRP). Secara umum pemodelan nurse rostering atau heathcare staff rostering harus memperhatikan batasan-batasan objek sehinga dapat menghasilkan hasil yang optimal. Masalah lain dari penjadwalan staf merupakan masalah keadilan antar staf yang bertugas, bagaimana pembagian alokasi libur, waktu kerja, atau tempat tugas menjadi dimensi yang perlu dipertimbangkan. Banyak Penelitian menyebutkan bahwa indeks kepuasan suatu perawat atau staf dalam bekerja dipengaruhi oleh tingkat keadilan dalam pembagian jadwal. Untuk menyelesiakan permasalahan tersebut, pada penelitian ini akan dilakukan penjadwalan dengan menggunakan algoritma tabu search hyperheuristic. Algoritma Tabu Search hyper-heuristic akan digunakan memberikan solusi terhadap masukan permasalahan dengan cara menghasilkan heuristik baru dengan menggunakan heuristic yang sudah ada. Hasil optimasi penjadwalan dengan algoritma tabu search hyper heuristics pada Penelitian ini dapat diterima. Semua hard constraint pada setiap unit dapat terpenuhi dan soft contrsaint yaitu nilai jains fairness pada masing-masing unit setelah optimasi dibandingkan hasil jadwal otomatis meningkat mendekati nilai keadilan total yaitu satu. Nilai JFI pada unit Farmasi meningkat sebesar 47%, unit Nicu & Ruang Bayi meningkat sebesar 48%, unit IGD meningkat sebesar 20%, unit SIM & RM meningkat sebesar 2%, unit Gizi & Café meningkat sebesar 23% dan Ruang Operasi meningkat sebesar 2%. ======================================================================================== Scheduling labor hospital or known as staff healthcare rostering is the complex problems that must be faced by each hospital. Hospitals must consider many aspects such as the number of nurses, the division of shifts, the cost, the chance of a holiday or leave of absence and other constraints. Because a lot of these considerati ons, the scheduling manually will be very difficult and can not give the optimal solution. It is necessary the existence of a mathematical model to facilitate the scheduling problems with finding the most optimal solution. The problem is known with the ter m nurse rostering problem (NRP). In general, the modeling of the nurse rostering or hea l thcare staff rostering should pay attention to the boundaries of the object so that it can produce optimal results. Another problem of staff scheduling is a matter of j ustice between the staff on duty, how the division of the allocation of holidays, working time, or place of duty be the dimensions that need to be considered. Many research mention that the satisfaction a nurse or staff in the work influenced by the level of fairness in the division of the schedule. To resolve these problems, this research will be done scheduling using tabu search algorithm hyperheuristic. Algorithm Tabu Search hyper - heuristic will be used to provide solutions to the input problems with how to generate a new heuristic using the heuristic that already exists. viii The results of the optimization of the scheduling with algorithm tabu search hyper heuristics on the research can be accepted. All hard constraints on each unit can be met and soft contr saint i.e. the value of the jains fairness on each unit after optimization compared to the results of the schedule of automatic increases approaching the value of justice, a total that one. The value of JFI on the Pharmaceutical unit increased by 47%, Nicu , & Baby Room increased by 48%, the unit of the Emergency room increased by 20%, SIM & RM units increased by 2%, unit of Nutrition & Café increased by 23% and the Operating Room increased by 2%

First-order Linear Programming in a Column Generation Based Heuristic Approach to the Nurse Rostering Problem

A heuristic method based on column generation is presented for the nurse rostering problem. The method differs significantly from an exact column generation approach or a branch and price algorithm because it performs an incomplete search which quickly produces good solutions but does not provide valid lower bounds. It is effective on large instances for which it has produced best known solutions on benchmark data instances. Several innovations were required to produce solutions for the largest instances within acceptable computation times. These include using a fast first-order linear programming solver based on the work of Chambolle and Pock to approximately solve the restricted master problem. A low-accuracy but fast, first-order linear programming method is shown to be an effective option for this master problem. The pricing problem is modelled as a resource constrained shortest path problem with a two-phase dynamic programming method. The model requires only two resources. This enables it to be solved efficiently. A commercial integer programming solver is also tested on the instances. The commercial solver was unable to produce solutions on the largest instances whereas the heuristic method was able to. It is also compared against the state-of-the-art, previously published methods on these instances. Analysis of the branching strategy developed is presented to provide further insights. All the source code for the algorithms presented has been made available on-line for reproducibility of results and to assist other researchers

Evolving comprehensible and scalable solvers using CGP for solving some real-world inspired problems

My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative Cartesian Genetic Programming can encode loops and nested loop with their termination criteria, making susceptible to evolutionary modification the whole programming construct. This newly developed extension and its application to metaheuristics are demonstrated to discover effective solvers for NP-hard and discrete problems. This thesis also extends Cartesian Genetic Programming and Iterative Cartesian Genetic Programming to adapt a hyper-heuristic reproductive operator at the same time of exploring the automatic design space. It is demonstrated the exploration of an automated design space can be improved when specific types of active and non-active genes are mutated. \\ A series of rigorous empirical investigations demonstrate that lowering the comprehension barrier of automatically designed algorithms can help communicating and identifying an effective and ineffective pattern of primitives. The complete evolution of loops and nested loops without imposing a hard limit on the number of recursive calls is shown to broaden the automatic design space. Finally, it is argued the capability of a learning objective function to assess the scalable potential of a generated algorithm can be beneficial to a generative hyper-heuristic

Optimasi Penjadwalan Staf Rumah Sakit Dengan Menggunakan Algoritma Simulated Annealing Hyper-Heuristic (Studi Kasus: RSIA Kendangsari MERR Surabaya)

Rumah sakit Ibu dan Anak Kendangsari merupakan salah satu rumah sakit swasta yang berada di wilayah Surabaya. Salah satu hal yang menjadi perhatian dalam manajemen rumah sakit adalah penjadwalan staf rumah sakit yang optimal guna memenuhi kebutuhan pasien selama 24 jam penuh. Permasalahan ini menjadi kompleks karena terdapat berbagai batasan yang harus dipenuhi yang terdiri atas hard constraints dan soft constraints. Selama ini rumah sakit masih menggunakan metode penjadwalan secara manual yang memakan banyak waktu. Maka dari itu dibutuhkan suatu penjadwalan otomatis yang membutuhkan waktu lebih sedikit untuk mencapai penjadwalan yang optimal. Penjadwalan yang optimal akan dilakukan dengan memaksimalkan nilai Jain’s Fairness Index dari libur yang didapat oleh setiap staf pada setiap unit. Unit-unit yang menjadi ruang lingkup adalah Unit Farmasi, Unit Ruang Bayi dan NICU, Unit SIM Rekam Medis dan Registrasi, Unit Gizi, Unit Rawat Jalan dan IGD serta Kamar Operasi. Untuk dapat menyelesaikan permasalahan ini maka penulis akan menggunakan metode simulated annealing. Simulated Annealing merupakan sebuah metode dengan analogi seperti proses annealing pada logam. Algoritma simulated annealing akan fokus terhadap pencarian solusi optimal dengan menerima adanya solusi yang lebih buruk ketika melakukan iterasi. Dalam pengerjaan metode ini, nantinya akan dilakukan bersama dengan metode hyper-heuristic. Metode hyper-heuristic berjalan pada lingkungan heuristic sehingga menghasilkan solusi yang lebih umum dibandingkan dengan penggunaan metode metaheuristics. Hasil dari penelitian ini adalah meningkatnya nilai Jain’s Fairness Index untuk setiap unit ketika dilakukan optimasi dengan menggunakan algoritma Simulated Annealing Hyper-Heuristic. Untuk Unit Farmasi, nilai JFI hasil manual meningkat dari 0.92 menjadi 0.93. Unit Ruang Bayi dan NICU hasilnya meningkat dari 0.89 menjadi 0.91. Unit SIM Rekam Medis dan Registrasi meningkat dari 0.90 menjadi 0.97. Unit Gizi meningkat dari 0.85 menjadi 0.86. Unit Rawat Jalan dan IGD meningkat dari 0.91 menjadi 0.93. Dan terakhir Unit Kamar Operasi meningkat dari 0.80 menjadi 0.97. Penggunaan algoritma Simulated Annealing Hyper-Heuristic diharapkan dapat memberikan manfaat dengan membuat jadwal yang optimal serta waktu yang dihabiskan untuk penjadwalan menjadi lebih cepat. ==================================================================================== RSIA Kendangsari is one of the private hospital located in Surabaya area. One of the main concerns in hospital management is the optimal hospital staff scheduling to meet the needs of patients for 24 hours. This problem becomes complex because there are various constraints that must be met consisting of hard constraints and soft constraints. During this time the hospital still uses manual scheduling which takes a lot oftime. Therefore it requires an automated scheduling that takes less time to achieve optimal scheduling. Optimal scheduling will be done by maximizing the value of Jain's Fairness Index from the holidays earned by each staff on each unit. The units that are included in this research are Pharmacy Unit, Infant and NICU Unit, Registration and Medical Record Information System Unit, Nutrition Unit, Outpatient and EmergencyUnit and Surgery Room. To be able to solve this problem then the author will use simulated annealing method. Simulated Annealing is a method with analogies such as annealing processes in metals. The simulated annealing algorithm will focus on finding the optimal solution by accepting a worse solution when iterating. In this method work, it will be done together with hyper-heuristic method. Hyper-heuristic methods run on a heuristic environment resulting in a more general solution than the metaheuristics method. The result of this research is the increase of Jain's Fairness Index value for each unit when optimized by using Simulated Annealing Hyper-Heuristic algorithm. For Pharmacy Unit, the JFI value of manual sceheduling increased from 0.92 to 0.93. The Infant and NICU Unit resulted in an increase from 0.89 to 0.91. Registration and Medical Record Information System Unit increased from 0.90 to 0.97. The Nutrition Unit increased from 0.85 to 0.86. Outpatient and Emergency Unit increased from 0.91 to 0.93. And Surgery Room Unit increased from 0.80 to 0.97. The use of the Simulated Annealing Hyper-Heuristic algorithm is expected to provide benefits by creating an optimal schedule and time spent on scheduling to be faster

A review on the self and dual interactions between machine learning and optimisation

Machine learning and optimisation are two growing fields of artificial intelligence with an enormous number of computer science applications. The techniques in the former area aim to learn knowledge from data or experience, while the techniques from the latter search for the best option or solution to a given problem. To employ these techniques automatically and effectively aligning with the real aim of artificial intelligence, both sets of techniques are frequently hybridised, interacting with each other and themselves. This study focuses on such interactions aiming at (1) presenting a broad overview of the studies on self and dual interactions between machine learning and optimisation; (2) providing a useful tutorial for researchers and practitioners in both fields in support of collaborative work through investigation of the recent advances and analyses of the advantages and disadvantages of different techniques to tackle the same or similar problems; (3) clarifying the overlapping terminologies having different meanings used in both fields; (4) identifying research gaps and potential research directions