A room-oriented artificial bee colony algorithm for optimizing the patient admission scheduling problem

Highlights

• Proposed an artificial bee colony with room-oriented approach to tackle the PAS problem.

• The population of solutions are randomly generated using room-oriented approach.

• Three neighbourhood searches are used by the ABC algorithm to navigate the search space of the PAS.

• The performance of the proposed ABC is compared with state-of-the-art that worked on the same dataset.

• The results showed that the proposed ABC is better for the PAS when compared with the state-of-the-art.

Abstract

Patient admission scheduling (PAS) is a tasking combinatorial optimization problem where a set of patients is assigned to limited facilities such as rooms, timeslots, and beds subject to satisfying a set of predefined constraints. The investigations into the performance of population-based algorithms that utilized to tackle the PAS problem considered in this paper reveal their weaknesses in obtaining quality solutions that create a space to investigate the performance of another population-based method. Thus, in this paper, an Artificial Bee Colony Algorithm (ABC) is proposed to tackle the formulation of the PAS problem under consideration. It is a class of swarm intelligence metaheuristic algorithms based on the intelligent foraging behaviour of honey bees developed to solve continuous and complex optimization problems. Due to the discretization of the PAS, the continuous nature of the ABC algorithm is changed to cope with the rugged solution space of the PAS. The initial feasible solution to the PAS problem is obtained using the room-oriented approach. Then the ABC algorithm optimizes the feasible solutions with the aid of three neighbourhood structures embedded within the employed bee and the onlooker bee operators of the algorithm. The performance of the proposed ABC algorithm based on three different parameters, the solution number (SN), limit value (LV), and the maximum cycle number (MCN) is evaluated on six standard benchmark datasets of the PAS. Two of these main parameters (i.e. SN and LV) are fine-tuned to obtain the best solutions on instances like Test-data 1 = 679.80, Test-data 2 = 1180.40, Test-data 3 = 787.40, Test-data 4 = 1198.60, Test-data 5 = 636.80, and Test-data 6 = 818.60. The best solutions obtained by the proposed method are evaluated against the results of the 19 comparative algorithms comprising five population-based methods, eleven heuristic, and hyperheuristic-based methods, and three integer programming-based methods. The proposed method shows its supremacy in the performance by achieving the best results in all the instances of the dataset when compared with five population-based methods (DFPA, HSA, MBBO-GBS, BBO-GBS, and BBO-RBS) and producing the best results in five instances when compared with eleven heuristic and hyperheuristic-based methods (LAHC, DHS-GD, HTS, DHS-SA, ADAPTIVE GD, GD, HH-GD, DHS-IO, HH-SA, HH-IE, TA) and Finally, it had a competitive performance with the other three Integer programming methods (MIP warm start, MIP-Heuristic, CG) that worked on the same formulations of the PAS. In a nutshell, the proposed ABC algorithm could be adopted as a new template algorithm for the PAS community.

Introduction

The ultimate goal of a hospital care provider is to provide an efficient and high-quality service to its clients. However, the frequent surge in the population of clients seeking such services is thus making the goal increasingly more difficult to attain without some specific automated systems, especially in managing its limited resources among the various entities and events competing for such services. One area in the hospital where such automation is crucial is in the management of patients seeking admission into a hospital. The patient admission scheduling (PAS) problem, as it is usually called, is one of the challenging scheduling problems faced by many medical institutions that deal with finding an optimal way of assigning the hospital resources (such as beds, rooms, timeslots, and so on) to patients seeking the hospital admission while meeting all the necessary hospital requirements. Such hospital requirements or policy may differ from one hospital to another but could include that patients in a room must be of the same gender, accommodating patients could make a special room request, etc. Formally, PAS as a class NP-hard problem that belongs to the category of combinatorial scheduling problem entails the assignment of limited resources like rooms, beds, specialism, and timeslots to a number of patients so as to satisfy a set of restrictions [1]. Note that in a PAS problem, the number of given constraints are typically categorized into soft and hard. The constraint which needed to be satisfied for the PAS solution to be feasible is called the hard constraints while the violation of soft constraint is allowed in a feasible solution to the PAS. However, the reductions of such violations should be carried out to the barest minimum. The quality of the solution to the PAS is measured by the violations of soft constraints in a feasible PAS solution and the objective is to produce a high-quality solution to the PAS problem that satisfies the required constraints (i.e feasible solution). It is worthy of mentioning that studies have proven that it is almost impossible to optimize a feasible solution to the PAS to the tune of satisfying all the soft constraints [2]. Different formulations of the PAS have been proposed and investigated over the last few decades. Few examples of the literature that worked on formulations of other hospital versions can be studied in [3], [4], [5]. Similarly, the most widely investigated formulation of the PAS problem developed in [6] and investigated by [7] is the focus of this study.

The patient admission scheduling problem (PAS) has drawn the attention of research communities in the field of timetabling, scheduling, and operational research over the last few years in which numerous studies have proposed several methodologies to tackle the PAS problem. Several artificial intelligence approaches introduced over the years are traditional-based methods, metaheuristic-based methods, hyper-heuristic methods, and hybrid-based methods. Some examples of commonly used traditional methods are column generation-based approach [8], [9], mixed-integer programming [10], [11] and linear programming-based approach [3], while those employed under metaheuristic-based are classified into two: local search-based and population-based methods. Few examples of the local search-based algorithm are adaptive non-linear great deluge algorithm [12] and simulated annealing (SA) [1], [13], [14]. Furthermore, the techniques that made used of population-based include genetic algorithm (GA) [4], [5] biogeographical-based optimization algorithm [15], [16], [17], and harmony search algorithm [18]. Similarly, the usage of hyper-heuristic techniques for the PAS problem has been reported in [7], [19] and lastly, the hybrid-based approach utilized to tackle the PAS problem can be found in [20]. Other studies on patient admission scheduling problems can be found in [21], [22], [23], [24].

A critical analysis of existing techniques that worked on the instances of the PAS under consideration from the literature revealed that the results obtained by the population-based metaheuristics like BBO [15], [16], [17] and HSA algorithms [18] are not as good as those obtained by other techniques. This is due to the fact that these algorithms tend towards the exploration of the solution space rather than exploitation and thus lose the capability of exploiting the rugged nature of the search space of the PAS. In view of the above, the motivation of this study is to introduce a new population-based swarm intelligence algorithm with the incorporation of efficient neighbourhood structures for tackling the PAS problem.

In 2005, Karaboga introduced Artificial Bee Colony (ABC) algorithm as a population-based metaheuristic to solve practical optimization problems [25]. It is relatively a new nature-inspired optimization algorithm that simulates the intelligent foraging behaviour of honey bees in their hive. Experimentally, ABC has the advantage of utilizing fewer control parameters, it has a competitive performance in comparison with other swarm intelligence-based techniques. The simplicity and ease of implementation of the ABC motivated its very high utilization in solving many practical combinatorial optimization problems [26]. Few examples of the complex optimization problems in which the success of ABC have been recorded are timetabling problems [27], [28], [29], Job shop scheduling problem [30], Vehicle routing problem [31], travelling salesman problem [32], protein structure prediction [33], and well placements in fractured reservoirs [34]. Note that other notable areas of application of the ABC algorithm can be found in [26], [35]. Based on the competitive performance of the ABC algorithm, therefore, the main contribution of this paper is to adapt the ABC algorithm with the integration of efficient and simple neighbourhood searches to its operators as an alternative solution template to the research community when utilized to tackle the PAS problem. The performance of the proposed ABC algorithm for the PAS problem is evaluated using the popular Benchmark dataset of the PAS consists of 13 real-world problem instances as proposed in [6] and investigated in [7]. It is noteworthy that the proposed ABC algorithm is tested on the six most widely utilized instances from this benchmark dataset. The results of the experiment produced by the proposed ABC method achieved the first rank when compared with population-based and other heuristic methods and came third in comparison with hybrid integer programming methods

The outline of this paper is presented as follows: the descriptions and formulations of the PAS are provided in Section 2 while Section 3 discusses an overview of the ABC algorithm. Section 4 describes the adaptation of the proposed ABC algorithm for the PAS problem and presentation of the experimental analysis, discussion of results, and comparison with other state-of-the-art techniques are discussed in Section 5. Lastly, the conclusion and future directions are presented in Section 6.