Timetabling Algorithm Research Articles

Construction of kill webs with heterogeneous UAV swarms in dynamic contested environments

With the concept of "mosaic warfare," a novel combat style that involves constructing "kill webs" with unmanned aerial vehicle (UAV) swarms has emerged. However, little research has focused on this specific task scenario, particularly concerning the self-organization and adaptive collaboration of heterogeneous combat units in dynamic contested environments. Considering the scales and highly dynamic natures of such swarms, an adaptive communication network mechanism is developed based on the Molloy-Reed criterion. In contrast with common offline/noncombat task scenarios, the self-organization process is refined through agent-based modeling, and a combat effectiveness evaluation is introduced to provide enhanced task execution incentives. The proposed dynamic consensus-based coalition algorithm (DCBCA) addresses UAV intelligence defects such as "confusion," "forgetfulness," and "recklessness" during the dynamic target selection process, enabling effective bottom-up kill webs construction. Extensive simulation results demonstrate that the algorithmic system outlined in this paper can support the efficient and resilient operations of large-scale heterogeneous UAV swarms. The DCBCA outperforms the dynamically improved consensus-based grouping algorithm (CBGA) and the consensus-based timetable algorithm (CBTA) in terms of performance and convergence speed.

Instance Space Analysis for Algorithm Testing: Methodology and Software Tools

Instance Space Analysis (ISA) is a recently developed methodology to (a) support objective testing of algorithms and (b) assess the diversity of test instances. Representing test instances as feature vectors, the ISA methodology extends Rice’s 1976 Algorithm Selection Problem framework to enable visualization of the entire space of possible test instances, and gain insights into how algorithm performance is affected by instance properties. Rather than reporting algorithm performance on average across a chosen set of test problems, as is standard practice, the ISA methodology offers a more nuanced understanding of the unique strengths and weaknesses of algorithms across different regions of the instance space that may otherwise be hidden on average. It also facilitates objective assessment of any bias in the chosen test instances and provides guidance about the adequacy of benchmark test suites. This article is a comprehensive tutorial on the ISA methodology that has been evolving over several years, and includes details of all algorithms and software tools that are enabling its worldwide adoption in many disciplines. A case study comparing algorithms for university timetabling is presented to illustrate the methodology and tools.

Hybrid Erosion And Deposition Metaheuristic University Teaching Timetabling Framework

The research developed a Hybrid Erosion And Deposition Metaheuristic University Teaching Timetabling Algorithm (HEADMUTTA). The hybrid erosion and deposition metaheuristic university teaching timetabling algorithm constructs a university teaching timetable with very few iterations. The Hybrid Erosion And Deposition (HEAD) metaheuristic university teaching timetabling algorithm adopts its behaviour from the HEAD metaheuristic with some concepts adapted from Tabu Search, Simulated Annealing, and Ant Colony metaheuristics. The HEADMUTTA constructs a draft university teaching timetable and further improves it by searching for the best feasible solution that satisfies the predetermined soft and hard rules or constraints. The research also proposed a Hybrid Erosion and Deposition Metaheuristic University Teaching Timetabling framework for implementation. The results indicate that the use of hybrid metaheuristics to solve university teaching timetabling problems improves the quality of the produced university teaching timetables. The HEAD metaheuristic algorithm has a unique feature that allows it to further improve the draft university teaching timetable. Further improvements in the framework may reduce the complexity of NP-hard combinatorial teaching timetabling problems.

Flowshop scheduling problem with objective of minimizing TCT

In manufacturing industries, scheduling problems are the origin. Particularly flowshop scheduling problem occurs in time table algorithm, operatory theory and combinatorial optimization problem with the total completion time (TCT) minimizing is a herculean task to obtain near optimal solution. Researchers are interested in solving these types of problems with the objective being that TCT is quite fashionable. Comparing the solution with existing one is quite logical to arrive the conclusion which algorithm performance better than the other. The heuristic approach developed by us, Jayakumar and Vasudevan performs better compare with other algorithms found in the literature.

Consensus-Based Decentralized Task Allocation for Multi-Agent Systems and Simultaneous Multi-Agent Tasks

This letter proposes a novel consensus-based timetable algorithm (CBTA) to solve the decentralized simultaneous multi-agent task allocation problem. Due to the limited capability of each agent, multiple agents may be required to perform a task simultaneously. A key challenge is how to meet the requirements and minimize the average start time of all tasks. The proposed CBTA aims to minimize the start time of each task to minimize the average start time of all tasks indirectly, it iterates between a timetable construction phase and a consensus phase. New tasks are included in the timetable of each agent by comparing the estimated start time of tasks placed by its own and other agents during the timetable construction phase. Then in the consensus phase, agents share their timetables with a communication network, and conflicts among their timetables are eliminated according to a consensus rule. Extensive simulation results show that the average start time of tasks of the proposed CBTA is nearly the same as the consensus-based bundle algorithm (CBBA) when performing single-agent tasks, and it is much less than the consensus-based grouping algorithm (CBGA) when performing multi-agent tasks with various communication network topologies.

A genetic algorithm for heterogeneous high-speed railway timetabling with dense traffic: The train-sequence matrix encoding scheme

Recently, the continued growth of passenger demand for high-speed railways and expectations for varied types of train services have posed a great need for designing a railway timetable suitable for dense and heterogeneous train traffic, where train overtaking is necessary for proper capacity utilization. This study develops an efficient genetic algorithm that considers train orders in all sections to better depict train overtaking and impose specific operational rules essential in this context. Train-sequence matrix is chosen as the chromosome encoding, based on which the “exchange + regeneration” matrix crossover operator is innovatively designed that considers the heterogeneity among trains and improves the feasibility of the crossover, which previous one-sequence crossover operators cannot realize. An overtaking-oriented local search heuristic is inserted in the algorithm to facilitate the local improvement. To guarantee the feasibility of the final solution, a conflict resolution procedure with conflict impact area identification is introduced. Tests of the algorithm on several small- and medium-sized cases reveal that it can reach relatively good solutions within a short time. Finally, the algorithm is tested on Beijing-Shanghai high-speed railway corridor in China and presents good performance both in efficiency and quality.

An efficient and exact algorithm for military timetabling and trainee assignment problems

We present an efficient and exact algorithm for timetabling military training — a novel integration of Knuth’s efficient Dancing Links indexing scheme with A∗ search that allows us to simultaneously schedule and optimally assign military trainees to classes while respecting domain constraints. We show that our Simultaneous Sequencing and Assignment Solver (SSAS) is able to handle cohort sizes appropriate to the requirements of the Australian Defence Force under a complex prerequisite structure for the courses. Comparisons using real-life parameters with the best known integer programming approach (a column generation-based heuristic) has showed a significant computational benefit from using SSAS. We further tested our method on larger problem instances that might arise in larger training schools. Our SSAS was able to optimally solve such larger-scale problems or prove the problem infeasible in a reasonable computation time.

Joint optimization of timetabling, vehicle scheduling, and ride-matching in a flexible multi-type shuttle bus system

Shuttle bus services play a vital role in public transit systems. However, conventional shuttle bus systems use the same type of buses and fixed departure timetables. They fail to meet the time-varying travel demand and do not consider the diversified characteristics of transit passengers. With the advent of the information era, communication among passengers, buses, and dispatching centers has become much easier. Accordingly, demand-responsive bus dispatching methods are expected to increase the flexibility of operation schemes to improve the performance of shuttle bus systems. To this end, this study proposes a mixed-integer linear programming model to incorporate ride-matching and shuttle bus dispatching in one framework. The bus trip schedules (including the number of used bus trips of different types, departure times, dwelling stops with dwelling times, and recommended travel speeds between adjacent stops of each trip) and passenger-to-vehicle matching schemes are optimized. The commonly used stop-skipping tactic, speed adjustment, and bus holding strategies are introduced to improve the flexibility and operational efficiency of shuttle bus systems. The objective is to minimize the weighted total passenger waiting times, passenger in-vehicle times, and operating costs. A modified Lagrangian relaxation algorithm is designed to improve computational efficiency for large-scale problems. A rolling horizon scheme is designed to implement the algorithm dynamically. It updates the dispatching scheme horizon by horizon according to newly collected requests, which can also improve the algorithm performance by reducing the problem scale. Numerical results show that the proposed flexible multi-type shuttle bus system outperforms a multi-type bus timetabling algorithm in all the considered cases, and it outperforms an on-demand ride-sharing algorithm in 80% of the cases.

Course Timetabling Problem during COVID-19: An Optimal Model Based on the Comparative Advantage of Online/Offline Education

COVID-19 has profoundly changed the way that we study and work. For students, especially primary and middle school students, online education has become a solution to learning problems. However, online and offline education have their own characteristics and different learning efficiencies in different disciplines, which in turn will bring different learning effects. Therefore, based on the learning styles and types of knowledge, we establish an optimization model by weighing the comparative advantages of online and offline learning, so as to make the best learning effect for students. Then, a course timetabling algorithm proposed verifies its feasibility through examples.

Solving no-wait job-shop scheduling problems using a multi-start simulated annealing with bi-directional shift timetabling algorithm

This paper presents a multi-start simulated annealing with bi-directional shift timetabling (MSA-BST) algorithm for solving the no-wait jobshop scheduling problem (NWJSP). To enhance the quality of the solution, a bi-directional shift timetabling procedure that allows delay timetabling and consequently enlarges the search space is embedded into the multi-start simulated annealing algorithm. The performance of the proposed MSA-BST algorithm is evaluated with respect to the makespan by comparing its computational results to those of the best-to-date meta-heuristic algorithm, the hybrid artificial bee colony (HABC) algorithm, in the literature. Experimental results that were obtained by applying the proposed algorithm to a set of benchmark problems in the literature indicate that it significantly outperforms HABC. The main contribution of this study is to provide a novel and effective alternative method for solving the complex NWJSP.

Heuristic Algorithm for Multi-Location Lecture Timetabling

This paper studies a real faculty timetabling problem with multi-location consideration. Faculty of Cognitive Sciences and Human Development, UNIMAS offers a master's program by coursework to postgraduate students. The construction of timetables for all the courses offered is a tedious process due to constraints such as team-teaching allocation, unavailability dates of lecturers, and multi-location considerations. Therefore, a manually designed timetable is not as practical as it is time consuming when operational constraints must be fulfilled. In this paper, a two-stage heuristic algorithm is proposed to solve this postgraduate coursework timetable problem. This is because the heuristic algorithm is easy to apply and able to generate a feasible solution in a short time. The proposed two-stage heuristic algorithm consists of Lecturer Grouping Stage and Group Allocation Stage. In Stage I, the lecturers are assigned into four lecturer groups with the condition of no identical lecturers in each of the groups. Then, in Stage II, these groups are allocated into a set of academic weeks throughout the semester. The timeslot for each course can be allocated, and the team-teaching slot for the lecturers can be assigned in this stage. The result from the two-stage heuristic algorithm shows remarkable improvement over the real timetables solution by analyzing the distribution of lecture sessions of the courses.

Scheduling of Flexible Manufacturing Systems Subject to No-Wait Constraints via Petri Nets and Heuristic Search

This article addresses the scheduling problem of deadlock-prone flexible manufacturing systems subject to no-wait constraints for the first time, and develops a new scheduling algorithm based on the place-timed Petri net (PN) model and heuristic search. The considered problem can be solved by two procedures: 1) timetabling and 2) sequencing. The timetabling is to translate a given job sequence into a feasible schedule that satisfies the deadlock-free and no-wait constraints. A novel timetabling algorithm based on the controlled PN model is then proposed for solving it. The goal of sequencing is to find a job sequence so that the makespan of the corresponding schedule is the minimum. To this end, a hybrid heuristic search (HHS) is developed by combining the A* algorithm and dynamic window. Two new heuristic functions are designed to guide the search, and the dynamic window is used to limit the searched space. The performance of HHS with different heuristic functions and deadlock controllers is evaluated by ten instances. The computational results demonstrate that through the proposed approach, optimal or suboptimal feasible schedules can be obtained within a reasonable time.

CB-Planner: A bus line planning framework for customized bus systems

A customized bus (CB) system is an emerging public transportation that aims to provide direct and efficient transit services for groups of commuters with similar travel demands. Existing CB systems aggregate similar travel demands and plan bus lines manually, which is inefficient and costly. In this paper, we propose a CB line planning framework called CB-Planner, which is applicable to multiple travel data sources. A mathematical programming formulation is proposed to simultaneously optimize bus stop locations, bus routes, timetables and passengers’ probabilities of choosing CB. We then developed a heuristic solution framework that includes a grid-density based clustering method for discovering potential travel demands efficiently, a bus stop deployment algorithm to minimize the number of stops and walking distance, and dynamic programming based routing and timetabling algorithms for maximizing estimated profit. We conduct an experiment on a small-scale network to verify the performance gap between the optimal solution and our proposed heuristic solution. A case study is then conducted on one-month taxi trajectory data in Nanjing, China. The study demonstrates that CB lines generated by our CB-Planner can achieve higher profit compared with baseline methods, and they also provide efficient transit services with short walk distances and small departure time adjustments. The moderate increase in travel time is paid off by the significant savings in travel fare.

A Model and Algorithm for Passenger-oriented Train Timetabling on Urban Rail Transit Network

This paper focuses on optimizing passenger train timetable on an urban transit network with given predetermined long and short routing operation mode. A double objective integer programming model is established in order to reduce the difficulty of solving train timetabling problem of large transit network. A Lagrangian relaxation algorithm was designed to decrease the complexity of solving the problem by transforming the complicated coupling problem into two independent sub-problems of trains and agents respectively. In response to two sub-problems of Lagrangian relaxation, a time-space network was constructed to solve the shortest path problem of passengers and trains by dynamic programming. Finally, the model and algorithm are verified and analyzed by a simple example.

A hybrid genetic algorithm with 2D encoding for the scheduling of rehabilitation patients

Abstract Owing to aging population, rehabilitation treatments are increasing important, yet the scheduling of rehabilitation patients has been received little research attention. Focusing on real needs for hospital management, this study aims to develop a hybrid genetic algorithm that integrates genetic algorithm and simulated annealing to solve the present problem effectively and efficiently. A novel 2-dimension encoding method was designed to represent for the sequence of patients and their operations. In addition, a timetabling algorithm was developed for decoding a sequence into the best solution efficiently. To validate the proposed approach, a number of experiments based on the real data in a medical center were designed for comparison. The results have shown the proposed approach with better performance than conventional approaches. An empirical study has shown practical viability of this approach.

Generating an optimal timetabling for multi-departments common lecturers using hybrid fuzzy and clustering algorithms

University course timetabling is a NP-hard problem that be performed for each semester frequently. In this paper, we use a two-step algorithm for timetabling of common lecturers among departments. In the first step, we use a fuzzy multi-criteria decision-making comparison and local search algorithms with seven neighborhood structures and random iteration. It means that we use a fuzzy multi-criteria comparison algorithm to eliminate the ambiguities and soft constraints of common lecturers among departments. In addition, we apply the local search algorithm with seven neighboring structures to avoid trapping into local optima and improve the fuzzy multi-criteria comparison over the preferences and soft constraints of lecturers. In the second step, the common lecturers’ timetable generated in the first step by the clustering approach (k-means, fuzzy c-means and funnel shape) is clustered based on the preferences and soft constraints of common lecturers among departments. Now, our common lecturers prepared by the clustering algorithms are mapped to the traversed free resources according to the paper’s aims: (1) descending satisfaction of preferences and soft constraints of common lecturers among departments and (2) minimizing the loss of extra resources of each faculty, so that an optimal instance of our common lecturers timetabling is generated among departments. The applied datasets are in terms of satisfying the scheduling requirements in the real world for multi-departments of Islamic Azad University of Ahar branch.

NEW EXAMINATION TIMETABLING ALGORITHM USING THE SUPERSTAR ASSIGNMENT TECHNIQUE

In this paper, a new examination timetabling algorithm, SAT, is introduced. In order to solve the current problems that SAT algorithm can meet the requirement under the limited of all related resources and factors. It combined with rules, constraints, exceptions and priorities. This algorithm works in three steps: pre-processing, creating superstars and getting rid of superstars. SAT mechanisms sort all related parameters and factors, then determine stars and superstars of each related parameter. Each iteration of algorithm is trying to assign all superstars of all parameters as targets for processing. As well as, the process mechanism is run for putting the output into a suitable timeslot. To prove the algorithm implementation, a dataset from semester 1/2016 of Registration Centre, Ramkhamhaeng University has been selected as test subject. This dataset consists of 20/2 days/periods, 85,000 registered students, 1,325 subjects, 813,253 seats, and 11/76/22,582 buildings/rooms/seats per day. The proposed model could be solved the current problems and shown details of subject such as the colour of answer sheet, room and so on. It could be done within less than two hours, meanwhile the current system took at least one month. For the future work, the large scale of algorithm is to be improved and developed into more dynamic version for a larger volume of data and handling more complicated constraints. Article DOI: https://dx.doi.org/10.20319/mijst.2018.33.253270 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Mixed-integer programming model and branch-and-price-and-cut algorithm for urban bus network design and timetabling

This study solves the simultaneous planning problem of network design and timetabling for urban bus systems. An innovative mixed-integer programming (MIP) model is formulated and a parallel branch-and-price-and-cut (BPC) algorithm is proposed to solve the problem. The key idea of the model formulation and the solution algorithm is to represent a bus timetable with a route and a dispatch pattern. An aggregation and greedy algorithm is developed to efficiently solve the pricing subproblem. The cuts of disaggregate coupling inequalities are dynamically added to strengthen the lower bound. A computational study is conducted to evaluate the performance of the proposed methodology. The comparison with alternative solution approaches indicates that the parallel BPC algorithm is superior to solving the MIP formulations with the off-the-shelf MIP solver. Different values of model parameters are also tested, and various statistics of operators and passengers are reported for the cases.

Resolving Infeasibilities in Railway Timetabling Instances

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes.

MILP formulations and a TS algorithm for reliable last train timetabling with uncertain transfer flows

This paper aims to develop reliable last train timetabling models for increasing number of successful transfer passengers and reducing total running time for metro corporations. The model development is based on an observation that real-world transfer flows capture the characteristics of randomness in a subway network. For systematically modelling uncertainty, a sample-based representation and two types of non-expected evaluation criteria, namely max–min reliability criterion and percentile reliability criterion are proposed to generate reliable timetables for last trains. The equivalent mixed integer linear programming formulations are deduced for the respective evaluation strategies by introducing auxiliary variables. Based upon the linearised models, an efficient tabu search (TS) algorithm incorporating solution generation method is presented. Finally, a number of small problem instances are solved using CPLEX for the linear models. The obtained results are also used as a platform for assessing the performance of proposed TS approach which is then tested on large Beijing Subway instances with promising results.