Local Search Metaheuristics Research Articles

Route Planning for Intra-Hospital Patient Transportation Using Metaheuristics and Mixed Integer Linear Programming.

Healthcare processes are complex and involve uncertainties to influence the service quality and health of patients. Patient transportation takes place between the hospitals or between the departments within the hospital (i.e., Inter- or Intra-Hospital Transportation respectively). The focus of our paper is route planning for transporting patients within the hospital. The route planning task is complex due to multiple factors such as regulations, fairness considerations (i.e., balanced workload amongst transporters), and other dynamic factors (i.e., transport delays, wait times). Transporters perform the physical transportation of patients within the hospital. In principle, each job allocation respects the transition time between the subsequent jobs. The primary objective was to determine the feasible number of transporters, and then generate the route plan for all determined transporters by distributing all transport jobs (i.e., from retrospective data) within each shift. Secondary objectives are to minimize the sum of total travel time and sum of total idle time of all transporters and minimize the deviations in total travel time amongst transporters. Our method used multi-staged Local Search Metaheuristics to attain the primary objective. Metaheuristics incorporate Mixed Integer Linear Programming to allocate fairly the transport jobs by formulating optimization constraints with bounds for satisfying the secondary objectives. The obtained results using formulated optimization constraints represent better efficacy in multi-objective route planning of Intra-Hospital Transportation of patients.

Energy-Aware Evolutionary Algorithm for Scheduling Jobs of Charging Electric Vehicles in an Autonomous Charging Station

The paper considers an innovative model of autonomous charging stations where a program implementing a scheduling algorithm and a set of jobs being scheduled are driven by the same common power source. It is assumed that one of the well-known local search metaheuristics—an evolutionary algorithm—is used for the scheduling process. The algorithm is designed to search for a sequence of charging jobs resulting in a schedule of the minimum length. Since processors with variable processing speeds can be used for computations, this has interesting consequences both from a theoretical and practical point of view. It is shown in the paper that the problem of choosing the right processor speed under given constraints and an assumed scheduling criterion is a non-trivial one. We formulate a general problem of determining the computation speed of the evolutionary algorithm based on the proposed model of a computational task and the adopted problem of scheduling charging jobs. The novelty of the paper consists of two aspects: (i) proposing the new model of the autonomous charging station operating according to the basics of edge computing; and (ii) developing the methodology for dynamically changing the computational speed, taking into account power and energy constraints as well as the results of computations obtained in the current iteration of the algorithm. Some approaches for selecting the appropriate speed of computations are proposed and discussed. Conclusions and possible directions for future research are also given.

An Iterated Local Search Metaheuristic for the Capacitated Demand-Driven Timetabling Problem

In many major cities, metro lines constitute the backbone of urban public transport, providing an efficient and greener alternative to private mobility. An important feature that distinguishes metro lines from other public transport means, such as buses, is that metros are typically tightly resource constrained. The trains operating on a particular line are often specifically fitted for that line, making any capacity expansion extremely costly and time-consuming. Therefore, researchers and operators alike are seeking ways to make better use of existing resources. One possible way of doing so is by adapting timetables to forecasted demand while accounting for limited vehicle capacities. Thus, we consider a demand-driven nonperiodic timetabling problem for a two-directional metro line that minimizes the total passenger waiting time through the efficient scheduling of the available trains. Considering that passengers board trains using a well-mixed policy, we explicitly account for train capacities on a moment-to-moment basis. Last, we consider that trains are allowed to short turn. In this respect, we assume that trains must pass by a given station before short turning and are only allowed to idle after having short turned. We devise a polynomial time algorithm for assessing the total passenger waiting time generated by a given timetable and an effective lower bound that is evaluated in linear time. These are used in a variable neighborhood search algorithm, which is embedded in an iterated local search metaheuristic. Classical local search-based neighborhoods are not effective for our problem because they do not explicitly handle the vehicle scheduling decisions. To handle this challenge, we proposed three tailored neighborhoods. We validate our heuristic on the uncapacitated version of the problem. Considering a benchmark of 48 artificial instances with up to 20 stations, our heuristic achieved an average gap of 0.67% and found eight new best solutions. We also validated our heuristic on three sets of instances based on realistic lines from Milan, Madrid, and Beijing. Furthermore, we demonstrate the operational advantages of our optimized timetables in the capacitated version of the problem by comparing them with regular timetables and with exact solutions obtained for the uncapacitated case. Furthermore, we conduct a sensitivity analysis with respect to the capacity of the trains and investigate the impact of a priority boarding policy. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0271 .

Adaptive local search algorithm for solving car sequencing problem

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines (MMAL) are often designed such that average station work satisfies the time allocated to each station, but some models with work-intensive options require more than the allocated time. Sequencing varying models in a mixed-model assembly line is the short-term decision problem that has the objective of preventing line stoppage resulting from a station work overload. Accordingly, a good allocation of models is necessary to avoid work overload. The car sequencing problem (CSP) is a specific version of the mixed-model sequencing problem that minimizes the work overload by controlling the sequence of models. In order to do that, CSP restricts the number of work-intensive options by applying capacity rules. Consequently, the objective is to find the sequence with the minimum number of capacity rule violations. In this study, we show that exact solution procedures are insufficient for application in industry. however, we provide five improved lower bounds for CSPLib instances by solving problems optimally with a subset of options. Additionally, we present four local search metaheuristics that are commonly used to solve CSP. The local search algorithms are compared over CSP benchmark instances, including CSPLib and ROADEF Challenge 2005. The computational experiments show that an Adaptive Local Search (ALS) provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Moreover, results show that the algorithmic effort should focus on randomly exploring more non-deteriorated solutions instead of systematic search or spending time visiting deteriorated solutions to escape local optima.

A Formulation for the Stochastic Multi-Mode Resource-Constrained Project Scheduling Problem Solved with a Multi-Start Iterated Local Search Metaheuristic

This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem.

Hybrid metaheuristics for the integrated and detailed scheduling of production and delivery operations in no-wait flow shop systems

In today's complex business environment, the optimisation of operational processes is an essential factor for the survival of organisations. Many companies struggling to maintain competitiveness search for better operational methods and models to minimise costs and improve market service levels. In these companies, the coordination between manufacturing and logistics activities is critical. The integration and synchronisation of these activities are alternatives that companies require to improve their operational performance and, consequently, increase customer service levels. This article contributes to this approach by proposing and evaluating new heuristic methods to solve the problem of scheduling production and distribution operations in no-wait flow shop systems integrated with transportation systems which operate with different distribution strategies. Based on the assumption that the improvement in synchronisation and coordination of production and transportation operations minimises delivery times and increases service levels, we propose and evaluate heuristic methods for the problem. These heuristic methods implement scheduling algorithmic structures based on the iterated greedy (IG), iterated local search, simulated annealing (SA), and variable neighbourhood search metaheuristics, which jointly schedule manufacturing and transportation operations. In this context, the decision level is operational. The minimum total flow time is the main optimisation criterion. The problem studied herein is inspired on the real-life case of an electronic goods company. The analysis of the experimental results demonstrates the potential of these methods to solve the problem of different models of transportation. Specifically, the IGSA2 method obtained the best results, improving the quality of the initial solutions by up to 17% in small, medium, and large instances depending on the adopted initialisation heuristic. The best proposed algorithm IGSA2 was compared with the two state-of-the-art algorithms to obtain superior results. The study also verified a proposed hypothesis to improve the quality of the solutions generated using heuristic methods, which was proved to be true for most of the experiments.

A mixed integer formulation and an efficient metaheuristic for the unrelated parallel machine scheduling problem: Total tardiness minimization

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for higher size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising. • A new mixed integer programming formulation for the Unrelated Parallel Machine Scheduling Problem. • The formulation uses positional variables, is linear and does not use the Big-M technique. • The formulation solves instances up to 150 jobs and 20 machines to optimality. • An efficient iterated local search metaheuristic is presented. • A potential issue in the commonly used instance-generation procedure is discussed and a new set of instances is proposed.

Optimization of the distance-constrained multi-based multi-UAV routing problem with simulated annealing and local search-based matheuristic to detect forest fires: The case of Turkey

Forests cover nearly a third of the Earth’s land area, and they are a key factor for all life on Earth, but unfortunately, forest fires are the greatest danger to their presence. The wildfires jeopardize general wellbeing, security, and require high levels of government resources. They also lead to noteworthy debasement of nature, property loss, and high rates of human death and injury. This paper proposes an algorithm to use and route unmanned aerial vehicles (UAVs) to mitigate forest fire risks. The developed matheuristic algorithm hybridizes simulated annealing and local search metaheuristics with an integer linear programming model. The mathematical model was developed to solve the distance-constrained multi-based multi-UAV routing problem, and because of the complexity of the problem, the generated metaheuristics helps the model to find better solutions. The effectiveness of the proposed matheuristic is tested with a real-life case study for Turkey and is also compared with a genetic algorithm. The Turkish State Meteorological Service generates forest fire-risk maps countrywide every day to predict fire risks 3 days later by using meteorological data. These maps are used to generate the risky regions to be visited by the UAVs, and the existing airports are considered for the UAVs to take off and land. The algorithm is coded using MATLAB and ILOG. The metaheuristics are designed with problem-based operators, and their parameters are tuned by experiments. Computational results demonstrate the effectiveness of the algorithm and the hybridization procedures. Results demonstrate that the CPU times for the methods are acceptable.

Automated design of search algorithms: Learning on algorithmic components

This paper proposes AutoGCOP, a new general framework for automated design of local search algorithms. In a recently established General Combinatorial Optimisation Problem (GCOP) model, the problem of algorithm design itself is defined as a combinatorial optimisation problem. AutoGCOP defines a general framework to optimise the composition of elementary algorithmic components as decision variables in GCOP. By modelling various well-known local search meta-heuristics within a general framework, AutoGCOP supports automatic design of new novel algorithms which may be highly different from those manually designed in the literature.Within the consistent AutoGCOP framework, various elementary algorithmic components are analysed for solving the benchmark vehicle routing problem with time window constraints and different characteristics. Furthermore, two learning models based on reinforcement learning and Markov chain are investigated to learn and enhance the compositions of algorithmic components towards the automated design of search algorithms. The Markov chain model presents superior performance learning the compositions of algorithmic components during the search, demonstrating its effectiveness designing new algorithms automatically.

Combining Heuristics with Simulation and Fuzzy Logic to Solve a Flexible-Size Location Routing Problem under Uncertainty

The location routing problem integrates both a facility location and a vehicle routing problem. Each of these problems are NP-hard in nature, which justifies the use of heuristic-based algorithms when dealing with large-scale instances that need to be solved in reasonable computing times. This paper discusses a realistic variant of the problem that considers facilities of different sizes and two types of uncertainty conditions. In particular, we assume that some customers’ demands are stochastic, while others follow a fuzzy pattern. An iterated local search metaheuristic is integrated with simulation and fuzzy logic to solve the aforementioned problem, and a series of computational experiments are run to illustrate the potential of the proposed algorithm.

A modified biogeography-based optimization algorithm with improved mutation operator for job shop scheduling problem with time lags

Abstract This paper addresses the job shop scheduling problem including time lag constraints. This is an extension of the job shop scheduling problem with many applications in real production environments, where extra (minimum and maximum) delays can be introduced between successive operations of the same job. It belongs to a category of problems known as NP-hard problem due to large solution space. Biogeography-based optimization is an evolutionary algorithm which is inspired by the migration of species between habitats, recently proposed by Simon in 2008 to optimize hard combinatorial optimization problems. We propose a hybrid biogeography-based optimization (HBBO) algorithm for solving the job shop scheduling problem with additional time lag constraints with minimization of total completion time. In the proposed HBBO, the effective greedy constructive heuristic is adapted to generate the initial population of habitat. Moreover, a local search metaheuristic is investigated in the mutation step in order to ameliorate the solution quality and enhance the diversity of the population. To assess the performance of HBBO, a series of experiments on well-known benchmark instances for job shop scheduling problem with time lag constraints is performed.

GLS and VNS based heuristics for conflict-free minimum-latency aggregation scheduling in WSN

ABSTRACT We consider a conflict-free minimum latency data aggregation problem that occurs in different wireless networks. Given a network that is presented as an undirected graph with one selected vertex (a sink), the goal is to find a spanning aggregation tree rooted in the sink and to define a conflict-free aggregation minimum length schedule along the arcs of the tree directed to the sink. Herewith, at the same time slot, each element of the network can either send or receive at most one message. Only one message should be sent by each network element during the whole aggregation session, and the conflicts caused by signal interference should be excluded. This problem is NP-hard and remains NP-hard even in the case when the aggregation tree is given. Therefore, the development of efficient approximation algorithms is very important for this problem. In this paper, we present new heuristic algorithms based on genetic local search and variable neighbourhood search metaheuristics. We conducted an extensive simulation that demonstrates the superiority of our algorithms compared with the best of the previous approaches.

Generating Local Search Neighborhood with Synthesized Logic Programs

Local Search meta-heuristics have been proven a viable approach to solve difficult optimization problems. Their performance depends strongly on the search space landscape, as defined by a cost function and the selected neighborhood operators. In this paper we present a logic programming based framework, named Noodle, designed to generate bespoke Local Search neighborhoods tailored to specific discrete optimization problems. The proposed system consists of a domain specific language, which is inspired by logic programming, as well as a genetic programming solver, based on the grammar evolution algorithm. We complement the description with a preliminary experimental evaluation, where we synthesize efficient neighborhood operators for the traveling salesman problem, some of which reproduce well-known results.

A biased-randomised algorithm for the capacitated facility location problem with soft constraints

This paper analyzes the single-source capacitated facility location problem (SSCFLP) with soft capacity constraints. Hence, the maximum capacity at each facility can be potentially exceed by incurring in a penalty cost, which increases with the constraint-violation gap. In some realistic scenarios, this penalty cost can be modelled as a piecewise function. As a result, the traditional cost-minimization objective becomes a non-smooth function that is difficult to optimise using exact methods. A mathematical model of this non-smooth SSCFLP is provided, and a biased-randomized iterated local search metaheuristic is proposed as a solving method. A set of computational experiments is run to illustrate our algorithm and test its efficiency.

Can off-the-shelf inertial measurement units measure gait kinematics in patients with gait limitations?

Interactive reoptimization is an approach for progressively adjusting a candidate solution in order to introduce aspects of a problem that have not been entirely captured by the optimization model. In this paper, a reoptimization problem is investigated in the context of staff scheduling. The proposed reoptimization problem is derived from a shift scheduling problem. For solving the initial optimization problem and its reoptimization extension a neutrality-based iterated local search method is proposed. The conducted computational experiments first compare the proposed method against results from the literature on the initial shift scheduling problem. For this first part of the computational experiments, the datasets of the first International Nurse Rostering Competition (INRC2010) are used. The results indicate that the neutrality-based local search method provides on average significantly better solutions than the compared methods on small instances of the benchmark and has similar performance to the best known method for larger instances. In a second part of the experiments, the proposed method is evaluated on the reoptimization problem variant. The results on this second analysis reveal the practical difficulty of adjusting a candidate solution and the need of a global optimization approach, such as the proposed one, for the reoptimization problem. The results also support the fact that the proposed neutrality-based iterated local search metaheuristic is efficient for reoptimizing solutions in a very short time.

Three Local Search Meta-Heuristics for the Minimum Interference Frequency Assignment Problem (MI-FAP) in Cellular Networks

The minimum interference frequency assignment problem (MI-FAP) plays an important role in cellular networks. MI-FAP is the problem of finding an assignment of a small number of frequencies to a large number of transceivers (TRXs) that minimizes the interferences level. The MI-FAP is known to be NP-Hard, thus it cannot be solved in polynomial time. To remedy this, researchers usually use meta-heuristic techniques to find an approximate solution in reasonable time. Here, the authors propose three meta-heuristics for the MI-FAP: a variable neighborhood search (VNS) and a stochastic local search (SLS) that are combined to obtain a third and a new one, which is called VNS-SLS. The SLS method is incorporated into the VNS process as a subroutine in order to enhance the solution quality. All three proposed methods are evaluated on some well-known datasets to measure their performance. The empirical experiments show that the proposed method VNS-SLS succeeds in finding good results compared to both VNS and SLS confirming a good balance between intensification and diversification.

A neutrality-based iterated local search for shift scheduling optimization and interactive reoptimization

Interactive reoptimization is an approach for progressively adjusting a candidate solution in order to introduce aspects of a problem that have not been entirely captured by the optimization model. In this paper, a reoptimization problem is investigated in the context of staff scheduling. The proposed reoptimization problem is derived from a shift scheduling problem. For solving the initial optimization problem and its reoptimization extension a neutrality-based iterated local search method is proposed. The conducted computational experiments first compare the proposed method against results from the literature on the initial shift scheduling problem. For this first part of the computational experiments, the datasets of the first International Nurse Rostering Competition (INRC2010) are used. The results indicate that the neutrality-based local search method provides on average significantly better solutions than the compared methods on small instances of the benchmark and has similar performance to the best known method for larger instances. In a second part of the experiments, the proposed method is evaluated on the reoptimization problem variant. The results on this second analysis reveal the practical difficulty of adjusting a candidate solution and the need of a global optimization approach, such as the proposed one, for the reoptimization problem. The results also support the fact that the proposed neutrality-based iterated local search metaheuristic is efficient for reoptimizing solutions in a very short time.

Efficient local search strategies for the Mixed Capacitated Arc Routing Problems under Time Restrictions with Intermediate Facilities

In this paper, we extend our previous work on greedy constructive heuristics for the Mixed Capacitated Arc Routing Problem under Time Restrictions with Intermediate Facilities (MCARPTIF) by developing efficient local search improvement heuristics for the problem. Five commonly used arc routing move operators were adapted for the problem, and basic local search implementations were tested on waste collection benchmark sets. Tests showed that despite the application of commonly used speed-up techniques, the local search implementations are very slow on large test instances with more than one-thousand required arcs and edges. In response, more advanced local search acceleration mechanisms from literature were adapted and combined for the MCARPTIF and tested on the same instances. On the large instances, the basic local search setups took between 15 min and 3 h to improve a single solution to local optima, whereas the accelerated implementations took at most 4 min while producing similar quality local optima. The best performing implementation made use of two existing acceleration mechanisms, namely Static-Move-Descriptors and Greedy-Compound-Independent-Moves. A third mechanism, Nearest-Neighbour-Lists was also tested and although it reduced execution times it resulted in local search terminating at worse quality local optima. Given the importance of local search within metaheuristics, the developed local search heuristics provide a significant contribution to arc routing. First, the implementations can be extended to and incorporated into metaheuristics for the MCARPTIF. Second, the acceleration mechanisms can be applied to existing local search metaheuristics for Capacitated Arc Routing Problems, thereby improving the efficiency of the metaheuristics and allowing them to better deal with large instances.

Instance Scale, Numerical Properties and Design of Metaheuristics: A Study for the Facility Location Problem

We present an in-depth computational study of two local search metaheuristics for the classical uncapacitated facility location problem. We investigate four problem instance models, studied for the same problem size, for which the two metaheuristics exhibit intriguing and contrasting behaviours. The metaheuristics explored include a local search (LS) algorithm that chooses the best moves in the current neighbourhood, while a randomised local search (RLS) algorithm chooses the first move that does not lead to a worsening. The experimental results indicate that the right choice between these two algorithms depends heavily on the distribution of coefficients within the problem instance. This is also put further into context by finding optimal or near-optimal solutions using a mixed-integer linear programming problem solver.

Local search metaheuristics for Capacitated Vehicle Routing Problem: a comparative study

Local search metaheuristics for Capacitated Vehicle Routing Problem: a comparative study