Iterated Local Search Algorithm Research Articles

Team orienteering with possible multiple visits: Mathematical model and solution algorithms

This study addresses a new team orienteering problem in which each point can be visited possibly multiple times with decreasing scores. The problem is to determine a set of routes from a starting to a finishing point within an allowed travel time limit for the objective of maximizing the total collected score. A mixed integer programming model is developed to represent the problem mathematically. Then, due to the complexity of the problem, a basic iterated local search (ILS) algorithm is proposed that incorporates the ordinary perturbation and local search operators. Then, it is improved in two ways: (a) an extended ILS algorithm with multi-visit based local search operators and (b) a hybrid ILS algorithm with a simulated annealing technique to permit non-improving moves in the local search step. To test the performance of the ILS algorithms, computational experiments were done on modified benchmark instances under the cases of linear, convex and concave score decreases, and the results show that the hybrid ILS algorithm improves the others significantly and also gives near optimal solutions for small sized test instances. Finally, a case study was done for a naval warship reconnaissance operation, and the results are reported.

Multi-Objective Optimization Flow Shop Scheduling Problem Solving the Makespan and Total Flow Time with Sequence Independent Setup Time

In this paper, a multi-objective permutation flow shop scheduling problem with sequence independent setup time is studied. The bi-objective function that we consider is a linear combination of the makespan and total flow time with a weighted factor for each criterion. We propose a set of exact and approximate methods to minimize the makespan and total flow time in our flow shop optimization problem case. Hence, our main goal is to find the sequence of jobs that minimizes the two criteria of makespan and total flow time. The purpose is to solve this problem, with a mixed integer linear programming model (MILP) and a collection of efficient metaheuristics for different sizes of instances. Moreover, three metaheuristics are used: the Genetic Algorithm (GA), the Iterative Local Search (ILS) algorithm and the Iterated Greedy (IG) algorithm. The three last algorithms GA, ILS and IG are suggested in two ways for exploring the neighborhood. In order to test the efficacy of our resolution approach, different series of instances containing n jobs and m machines are generated randomly ranging from small to relatively large instances. The examination of the suggested simulations allowed us to remark that, for large and medium-scale instances, IG based on the exploration of the neighborhood records the best performances in terms of comparison with the other metaheuristics.

A variant of the NSGA II for the speed scaling distributed flow shop scheduling problem with total tardiness minimisation

In this study, an energy-efficient distributed flow shop scheduling (DFSS) problem with total tardiness minimisation and machine-sequence dependent setup times is addressed. A mixed integer linear programming (MILP) model is proposed for the problem. A variant of the NSGA II algorithm is suggested for the solution of large scale problems. The proposed algorithm is compared with the state-of-the-art NSGA II, SPEA II, and multiobjective iterated local search algorithm. The computational results show that the proposed algorithm is efficient and effective for the problem. This is the first study to propose a heuristic algorithm for the distributed flow shop scheduling problem with total tardiness minimisation, speed scaling and setups.

A Bayesian network structure learning method for optimizing ordering search operator

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

Picker routing optimization of storage stacker based on improved multi-objective iterative local search algorithm

<p style='text-indent:20px;'>In the process of warehouse automation, the efficient picker routing strategy is one of the key factors to improve warehouse efficiency. According to the order and the picking characteristics of the warehouse stacker, the picker routing of the stacker is regarded as the prize-collecting vehicle routing problem (PCVRP). According to the path and order for stacker picking, we designed a picker routing optimization strategy based on improved multi-objective iterative local search (IMOILS) algorithm. An elite pool strategy was set to save the high-quality solutions in the iterative process, and the nondominated solutions in the iterative evolution were stored and updated. Adding the adaptive enhanced perturbation strategy was beneficial to the current solution to escape from local optimum. In the local search procedure, to limit the excessively large search space, the epsilon constraint was adopted to limit the significant deterioration in another objective direction. The computational results showed that the proposed algorithm is superior to the comparison algorithms in the number of nondominated solutions, the hypervolume, and the spacing metric, and the stability of the algorithm is also good, which not only verifies the effectiveness of the proposed algorithm, but also provides a feasible optimization scheme for the storage stacker's picker routing problem.</p>

A Comprehensive Motion Compensation Method for In-Plane and Out-of-Plane Motion in Dynamic Contrast-Enhanced Ultrasound of Focal Liver Lesions.

Contrast-enhanced ultrasound (CEUS) acquisitions of focal liver lesions are affected by motion, which has an impact on contrast signal quantification. We therefore developed and tested, in a large patient cohort, a motion compensation algorithm called the Iterative Local Search Algorithm (ILSA), which can correct for both periodic and non-periodic in-plane motion and can reject frames with out-of-plane motion. CEUS cines of 183 focal liver lesions in 155 patients from three hospitals were used to develop and test ILSA. Performance was evaluated through quantitative metrics, including the root mean square error and R2 in fitting time-intensity curves and standard deviation value of B-mode intensities, computed across cine frames), and qualitative evaluation, including B-mode mean intensity projection images and parametric perfusion imaging. The median root mean square error significantly decreased from 0.032 to 0.024 (p < 0.001). Median R2 significantly increased from 0.88 to 0.93 (p < 0.001). The median standard deviation value of B-mode intensities significantly decreased from 6.2 to 5.0 (p < 0.001). B-Mode mean intensity projection images revealed improved spatial resolution. Parametric perfusion imaging also exhibited improved spatial detail and better differentiation between lesion and background liver parenchyma. ILSA can compensate for all types of motion encountered during liver CEUS, potentially improving contrast signal quantification of focal liver lesions.

Cluster Expansion Method for Critical Node Problem Based on Contraction Mechanism in Sparse Graphs

The objective of critical nodes problem is to minimize pair-wise connectivity as a result of removing a specific number of nodes in the residual graph. From a mathematical modeling perspective, it comes the truth that the more the number of fragmented components and the evenly distributed of disconnected sub-graphs, the better the quality of the solution. Basing on this conclusion, we proposed a new Cluster Expansion Method for Critical Node Problem (CEMCNP), which on the one hand exploits a contraction mechanism to greedy simplify the complexity of sparse graph model, and on the other hand adopts an incremental cluster expansion approach in order to maintain the size of formed component within reasonable limitation. The proposed algorithm also relies heavily on the idea of multi-start iterative local search algorithm, whereas brings in a diversified late acceptance local search strategy to keep the balance between interleaving diversification and intensification in the process of neighborhood search. Extensive evaluations show that CEMCNP running on 35 of total 42 benchmark instances are superior to the outcome of KBV, while holding 3 previous best results out of the challenging instances. In addition, CEMCNP also demonstrates equivalent performance in comparison with the existing MANCNP and VPMS algorithms over 22 of total 42 graph models with fewer number of node exchange operations.

An iterated local search algorithm for community detection in signed networks

Community detection in signed networks has become a research hotspot in the area of network science recently. Since the classical problem has great significance for theoretical analysis and practical application, many heuristics or metaheuristics have been presented. Despite some progress and results that have been achieved, it remains an open challenge to identify community structure in large signed networks. In this paper, we propose a simple and effective iterated local search algorithm coupled with a powerful local search mechanism to solve the community detection problem. Due to the limitation of modularity in resolution, the modularity density criterion is adopted to find communities in signed networks. Extensive experiments have been conducted on synthetic and real-world networks. The statistical analyses demonstrate that the proposed algorithm can provide high-quality solutions compared to the state-of-the-art algorithms.

An Iterative Neighborhood Local Search Algorithm for Capacitated Centered Clustering Problem

The Capacitated Centered Clustering Problem (CCCP) is NP-hard and has many practical applications. In recent years, many excellent CCCP solving algorithms have been proposed, but their ability to search in the neighborhood space of clusters is still insufficient. Based on the adaptive Biased Random-Key Genetic Algorithm (A-BRKGA), this paper proposes an efficient iterative neighborhood search algorithm A-BRKGA&#x005F;INLS. The algorithm uses shift and swap heuristics to search neighborhood space iteratively to enhance the quality of solutions. The computational experiments were conducted in 53 instances. A-BRKGA&#x005F;INLS improves the best-known solutions in 23 instances and matches the best-known solutions in 15 instances. Moreover, it achieves better average solutions on multiple instances while spending the same time as the A-BRKGA&#x002B;CS.

3D Atomic Structure of Supported Metallic Nanoparticles Estimated from 2D ADF STEM Images: A Combination of Atom-Counting and a Local Minima Search Algorithm.

Determining the 3D atomic structure of nanoparticles (NPs) is critical to understand their structure-dependent properties. It is hereby important to perform such analyses under conditions relevant for the envisioned application. Here, the 3D structure of supported Au NPs at high temperature, which is of importance to understand their behavior during catalytic reactions, is investigated. To overcome limitations related to conventional high-resolution electron tomography at high temperature, 3D characterization of NPs with atomic resolution has been performed by applying atom-counting using atomic resolution annular dark-field scanning transmission electron microscopy (ADF STEM) images followed by structural relaxation. However, at high temperatures, thermal displacements, which affect the ADF STEM intensities, should be taken into account. Moreover, it is very likely that the structure of an NP investigated at elevated temperature deviates from a ground state configuration, which is difficult to determine using purely computational energy minimization approaches. In this paper, an optimized approach is therefore proposed using an iterative local minima search algorithm followed by molecular dynamics structural relaxation of candidate structures associated with each local minimum. In this manner, it becomes possible to investigate the 3D atomic structure of supported NPs, which may deviate from their ground stateconfiguration.

An iterative local search based hybrid algorithm for the service area problem

This article presents a hybrid algorithm for the service area problem. The design of service areas is one of the essential issues in providing efficient services in both the public and private sectors. For a geographical region with a number of small spatial units, the service area problem is to assign the service-demand units to the service-supply units such that each facility has a service area. The basic criteria for the service areas are the highest service accessibility, the contiguous service areas, and that the service demand does not exceed the service supply in each service area. A hybrid algorithm for the service area problem is proposed by extending iterative local search (ILS) algorithm with three schemes: population-based ILS, variable neighborhood descent (VND) search, and set partitioning. The performance of the algorithm was tested using 60 well-designed instances. Experimentation showed that the instances could be solved effectively and efficiently. The solutions found by the hybrid algorithm approximate optimal solutions or the lower bounds with an average gap of 0.15%.

An Algorithm Framework for Facility Service Districting Problem

Objectives Facility service districting problem(FSDP) refers to the design of facility service areas according to the facility locations and service capacities in a geographical region. The design criteria for service areas include the balance of service demand and supply, the highest service accessibility, and the spatial contiguity. The spatial contiguity is a necessity for satisfying some policies on public services, such as school districting and medical districting. However, solving the FSDP with contiguity constraints is challenging. We present a hybrid algorithm framework for solving the FSDP. Methods The algorithm is proposed based on the general local search algorithm and furtherly enhanced by multi-start, ruin-recreate, set-partitioning and other optimization strategies. The basic modules such as initial solution generation method, local search operators, solution perturbation, model building and solving, and search strategies, are provided in the framework. Using these building blocks, some exact, metaheuristic and hybrid algorithms could be implemented effectively. Five algorithms are implemented for the FSDP: Exact method by solving a mixed integer linear programming model, simulated annealing (SA) algorithm, iterative local search (ILS) algorithm, SA with set-partitioning, and ILS with set-partitioning. In addition, four instances are designed to test the algorithms. The instance size, supply-demand ratio, and geographic environment are considered in the instance design. Results There are several findings from computing experimentation: Optimal or near-optimal solutions of the instances could be obtained by CPLEX optimizer; high-quality solutions could be found by SA and ILS algorithms much more efficiently; the set-partitioning procedure is capable of improving the solution quality. Conclusions Based on the proposed algorithm framework, it is easy and flexible to design local-search based matheuristics and hybrid algorithms for the FSDP. High quality solutions could be obtained by coupling the local search with ruin-recreate perturbation and set-partitioning.

Late acceptance-based heuristic algorithms for identifying critical nodes of weighted graphs

Identifying critical nodes is an efficient way to analyze and apprehend the properties, structures, and functions of complex networks, which is a challenging NP-hard problem. This paper studies a node-weighted version of the critical node problem (NWCNP) that involves minimization of pairwise connectivity measure of a given node-weighted graph via the removal of a subset of nodes (i.e., critical nodes), subject to a budgetary constraint. In this paper, we present two effective iterated local search algorithms for NWCNP. Our proposed algorithms iterate through two complementary search procedures. A local search procedure adopting a constrained neighborhood and late acceptance strategy is employed to find a local optimum from a given starting solution. Then, a destructive–constructive perturbation procedure is used to escape from a local optimum. We conduct extensive computational experiments with two categories of 32 benchmark instances that reveal our proposed algorithms can achieve the best upper bounds for 28 instances and are highly competitive compared to baseline algorithm. In particular, our algorithms achieved better performance on the first category of instances with random weighting than that on the second category of instances with logarithmic weighting. We also investigate the influence of history length and perturbation coefficient on the performance of the proposed algorithms.

A HYBRID HEURISTIC ALGORITHM FOR SCHOOL DISTRICT DIVISION

Abstract. Single-school and multi-school district divisions are the two main ways to balance educational resources for enrollment in primary and secondary schools. A hybrid heuristic algorithm (M-ILS-SA) for school district division is proposed based on the combination of a Multi-Start Iterative Local Search (M-ILS) algorithm and a Simulated Annealing (SA) algorithm. According to the principle of “school grouping first and student assigning second”, a K-Medoids model is first used to implement school grouping. Then, the initial solution for each run of ILS that starts is generated by the region growth algorithm. After completing the neighborhood search, the SA algorithm is finally used to choose the optimal solution from the historically generated school districts identified by ILS. The experimental results show that the proposed M-ILS-SA algorithm can effectively reduce the total elapsed time and the number of over-enrolled students in each school district, and ensure spatial continuity in both single-school and multi-school district divisions.

Solving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Time

In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.

The Impact of Perturbation Mechanisms on the Operation of the Swap Heuristic

In this study, an attempt was made to assess the impact of the most popular perturbation movements (i.e. Multiple-Swap(2-2), Multiple-Shift(2-2) and Multiple-K-Shift(1)), as well as the number of their calls on the quality of solutions and the time in which Swap(2-1) heuristics returns them. For this purpose, the iterative local search algorithm (ILS) was triggered, in which Swap(2-1) heuristics has cooperated with a single perturbation mechanism. The number of perturbations was changed in the range from 1 to 30. Each time the time and the difference between the percentage improvement of the objective function value of the solution obtained utilizing the Swap(2-1) algorithm cooperating with the perturbation mechanism and this algorithm working alone was checked. Based on the results obtained, it was found that the overall level of improvement in the quality of the returned solution is similar when using all of the considered perturbation mechanisms (is in the range of 2.49% to 4.02%). It has been observed that increasing the number of initiated perturbations does not guarantee an improvement in the quality of the returned solution. Perturbation movements similar to the motion initiated by the local search algorithm do not significantly improve the solution (they only entail extending the duration of action). The structure of the study has the following form. The Introduction chapter provides information on the Vehicle Routing Problem. The chapter Research methods contain a description of ILS and Swap(2-1) approaches and perturbation mechanisms considered. The last two chapters include the results of tests and conclusions.

On a bi-criteria flow shop scheduling problem under constraints of blocking and sequence dependent setup time

In this paper, we propose a bi-criteria optimization model for a flow shop scheduling problem with permutation, blocking and sequence dependent setup time. Indeed, these constraints are the most encountered in the industrial field, which demands high command flexibility. The objective is the minimization of two criteria, in our case the makespan and the total tardiness combined in a single objective function with a weighting coefficient for each criterion. To solve this problem, we propose a mixed integer linear programming method and a set of different metaheuristics. The suggested metaheuristics are; the genetic algorithm, the iterated greedy metaheuristic and the iterative local search algorithm. This last algorithm is proposed in two ways of exploration of the neighborhood. To verify the effectiveness of our resolution algorithms, a set of instances with n jobs and m machines is randomly generated from small instances to relatively large size ones. The analysis of the suggested simulation model allowed us to note that the iterative local search algorithm gives good results compared to the iterative greedy algorithm. Moreover, it was found that the weighting parameter plays an essential role in the problem decision making. However, it was established that it is difficult to find a good solution that minimizes both criteria at once, a suitable compromise will be necessary to be adopted using the weighting coefficient.

Iterated local search method and mathematical model for sequence-dependent U-shaped disassembly line balancing problem

Disassembly lines play an important role in disassembling end-of-life products and retrieving the valuable components. Sequence-dependent time increments are inevitable due to the interactions between two tasks in some occasions. This research provides the first attempt to study the sequence-dependent U-shaped disassembly line balancing problem (SUDLBP) with multiple objectives. A mixed-integer programming model is developed to solve the small-size instances optimally, where new expressions are developed to formulate the AND/OR precedence relations. Due to the NP-hard nature of this problem, a simple and effective iterated local search algorithm is developed for the first time. This algorithm utilizes modified NEH heuristic to achieve a high-quality initial solution. A new local search technic with referenced permutation and two neighbor structures is also embedded into it to obtain the local optimum solution. Computational tests demonstrate that the U-shaped lines outperform traditional straight lines in terms of the objective values. The comparative study on two sets of instances demonstrates that the proposed method outperforms the CPLEX solver in search speed and achieves a competing performance in comparison with other eight re-implemented algorithms.

Iterated Local Search Algorithm for single and double runway aircraft scheduling problems in Terminal Area

We present an Iterated Local Search (ILS) algorithm for solving the single and double runway aircraft scheduling problems in terminal area. The main ideas and implementation methods of each step are described in detail. Applying the ILS algorithm to solve the instance used in the literature and compare the results of ILS with those of previous 4 algorithms. For the single runway problem, the ILS can find the previous best known result. For the double runway problem, the ILS can find a result better than the previous best known result.

A hybrid iterated local search algorithm with adaptive perturbation mechanism by success-history based parameter adaptation for differential evolution (SHADE)

ABSTRACTThe iterated local search (ILS) is exceptionally successful in combinatorial solution spaces. However, few research works have reported on the application of ILS in continuous problems. In this article, a new hybrid population-based iterated local search (HILS) algorithm is proposed for solving numerical optimization problems. The proposed hybrid method introduces both success-history based parameter adaptation for differential evolution (SHADE) and limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) as the perturbation and local search strategy, respectively, and integrates the benefits of exploration capability of SHADE and local search performance of LBFGS. The simulated annealing type of acceptance criterion is adopted to balance the exploration and exploitation of ILS. The proposed HILS is tested against the CEC2017 benchmark functions, which were used to evaluate the performance of the proposed algorithm in solving numerical optimization problems. The experimental results show the effectiveness and efficiency of the HILS.