Efficient Local Search Procedure Research Articles

The constrained permutation flowshop problem: An effective two-stage iterated greedy algorithm to minimize weighted tardiness

In the domain of just-in-time permutation flowshop scheduling, most studies typically assume that all jobs either have their own soft due date or none of them do. However, in practice, scheduling a combination of hard and soft due date jobs, particularly with the context of emergency order insertion, remains a significant research topic. This paper addresses a constrained permutation flowshop scheduling problem with a mix of hard and soft due date jobs under total weighted tardiness criterion (CPFSP-TWT). We establish a mathematical model and propose an effective Two-Stage Iterated Greedy (ETSIG) algorithm tailored to the problem's characteristics, incorporating a two-stage constructive heuristic to generate a high-quality initial solution. We introduce problem-specific acceleration mechanisms based on position-bound considerations to enhance operational efficiency. We propose three knowledge-based repair strategies for handling infeasible solutions, along with a dynamic self-adjustment mechanism. Additionally, three efficient local search procedures integrate several specific perturbation operators to balance algorithmic exploitation and exploration abilities. Experimental evaluations affirm ETSIG's superiority over five state-of-the-art metaheuristics from closely related literature, establishing its efficacy in addressing CPFSP-TWT.

A parallel branch-and-cut and an adaptive metaheuristic to solve the Family Traveling Salesman Problem

This paper addresses the Family Traveling Salesman Problem (FTSP), a variant of the Traveling Salesman Problem that group nodes into families. The goal is to select the best route by visiting only a subset of nodes from each family. We developed two methods to solve the FTSP: (i) a parallel branch-and-cut algorithm with an efficient local search procedure (P-B&C) to obtain an optimal solution, and (ii) an adaptive metaheuristic that combines the Biased Random-key Genetic Algorithm (BRKGA) with a reinforcement learning algorithm. In this case, the Q-Learning algorithm controls the parameters of the BRKGA during the evolutionary process. We perform computational experiments on a well-known benchmark dataset with 185 instances. Our P-B&C proves the optimal value for 179 instances, improving the best upper bounds in 19 open instances. The new local search component of the P-B&C finds the best upper bounds for 50% of instances. The BRKGA-QL finds the optimal solution in 131 instances, improving the best upper bounds in 21 open instances. Finally, we compare our results with the best results in the literature, and both methods show robustness and efficiency in solving the FTSP.

Self-adaptive CMSA for solving the multidimensional multi-way number partitioning problem

The multidimensional multi-way number partitioning problem takes as input a set of n vectors with a fixed dimension m≥2, and aims to find a partitioning of this set into k≥2 non-empty subsets, such that the sums per coordinate across all subsets are as similar as possible. The problem has applications in key encryption, multiprocessor scheduling, minimization of circuit size and delay, and clustering. This paper employs a hybrid meta-heuristic, a self-adaptive version of the Construct, Merge, Solve, and Adapt algorithm equipped with an efficient local search procedure. Local search was able to accelerate the convergence towards promising regions of the search space. A comprehensive experimental evaluation shows that the proposed algorithm improves over all four competing algorithms from the related literature, especially when it comes to instances with higher k-values, i.e. k≥3. The observed average relative differences are for several instance groups larger than 25% in favor of the proposed algorithm compared to the second-best approach. In fact, a statistical evaluation indicates that our algorithm performs significantly better than the other approaches on all instances with k≥3.

A Memetic Algorithm for Curvature-Constrained Path Planning of Messenger UAV in Air-Ground Coordination

This paper addresses a UAV path planning problem for a team of cooperating heterogeneous vehicles composed of one unmanned aerial vehicle (UAV) and multiple unmanned ground vehicles (UGVs). The UGVs are used as mobile actuators and scattered in a large area. To achieve multi-UGV communication and collaboration, the UAV, modeled as a Dubins vehicle, serves as a messenger to fly over the effective communication range of all UGVs to relay information. The curvature-constrained path planning of the messenger UAV is formulated as a Dubins Traveling Salesman Problem with Dynamic Neighborhood (DTSPDN) which is a complex optimization problem involving coupled variables and contains dynamic constraints. We design an effective memetic algorithm to find the shortest route that enables the messenger UAV to visit all moving UGVs. This algorithm combines the genetic algorithm procedure, two kinds of local search operators based on gradient search and uniform sampling respectively, and a gradient-based repair operator to repair the solutions violating dynamic constraints. During the evolutionary process, a special phenomenon may occur that changing some decision variables (i.e., visiting sequence and location) may not affect the evaluation function value, but may alter the feasible region of another decision variable (i.e., visiting time) due to the encounter constraint between the UAV and UGV. To track and utilize the change of the feasible region, a transformation procedure is proposed to change one solution to another with less visiting time by analyzing the encounter pattern between UAV and UGV. The computational results on random instances with different scales demonstrate that the proposed approach can effectively generate better curvature-constrained tours to encounter all moving UGVs when compared to other four competitive algorithms in the literature. Note to Practitioners—This paper studies an emerging path planning problem for a UAV which is used to provide communication service for multiple moving UGVs. These UGVs are required to execute tasks (e.g., firefighting, search and rescue) within a large area. Due to their limited communication capabilities, they may be unable to obtain necessary information from other UGVs. The UAV serves as a messenger to fly over the effective communication range of all moving UGVs to relay information. We propose a novel memetic algorithm to efficiently search for the shortest tour that enables the messenger UAV to visit all moving UGVs. The memetic algorithm combines the parallel global search virtue of genetic algorithm with efficient local search procedure to improve the generated tour. A gradient-based repair procedure is also employed to make sure that the planned tour can guide the UAV to sequentially encounter each moving UGV. Simulations exhibit that the proposed approach can effectively generate high-quality tours for messenger UAV to rapidly visit all UGVs, which assists UGVs to achieve collaboration in large area. In future work, the proposed memetic algorithm will be extended to plan tours for multiple messenger UAVs.

Multi-Objective GRASP for Maximizing Diversity

This work presents a novel greedy randomized adaptive search procedure approach for dealing with the maximum diversity problem from a multi-objective perspective. In particular, five of the most extended diversity metrics were considered, with the aim of maximizing all of them simultaneously. The metrics considered have been proven to be in conflict, i.e., it is not possible to optimize one metric without deteriorating another one. Therefore, this results in a multi-objective optimization problem where a set of efficient solutions that are diverse with respect to all the metrics at the same time must be obtained. A novel adaptation of the well-known greedy randomized adaptive search procedure, which has been traditionally used for single-objective optimization, was proposed. Two new constructive procedures are presented to generate a set of efficient solutions. Then, the improvement phase of the proposed algorithm consists of a new efficient local search procedure based on an exchange neighborhood structure that follows a first improvement approach. An effective exploration of the exchange neighborhood structure is also presented, to firstly explore the most promising ones. This feature allowed the local search proposed to limit the size of the neighborhood explored, resulting in an efficient exploration of the solution space. The computational experiments showed the merit of the proposed algorithm, when comparing the obtained results with the best previous method in the literature. Additionally, new multi-objective evolutionary algorithms derived from the state-of-the-art were also included in the comparison, to prove the quality of the proposal. Furthermore, the differences found were supported by non-parametric statistical tests.

Effective constructive heuristic and iterated greedy algorithm for distributed mixed blocking permutation flow-shop scheduling problem

Distributed permutation flow-shop scheduling problem (DPFSP) has achieved much attention in recent years, which always assumes that there are infinite buffers between any consecutive machines. However, in many practical industrials, no buffers exist between some consecutive machines due to space constraint or technological requirement, which generate various types of blocking constraint. Hence, a distributed mixed permutation blocking flow-shop scheduling problem (DMBPFSP) is investigated in this paper, which considers three types of blocking constraint and without blocking. The objective is to minimize the maximum makespan among all factories. To address this problem, an improved NEH heuristic (NEH_P) is proposed, which incorporates the re-optimization of partial solutions. Afterwards, an efficient iterated greedy (EIG) algorithm is proposed. In the proposed EIG, the NEH_P heuristic is employed to generate the initial solution with high quality. A problem-specific knowledge based destruction–construction is used to explore the solution space. Three efficient local search procedures are designed to implement exploitation around the critical factory and exploitation across multi-factory. We compare the proposed methods against the closely relevant and high-performing methods in the literature. The computational results indicate that both NEH_P and EIG are very effective for addressing the considered problem.

A variable neighborhood search algorithm for transshipment scheduling of multi products at a single station

In this research, we investigate a transshipment scheduling problem in which a set of loading and unloading jobs must be performed at a single station of a transshipment terminal. We assume that there is a set of product types and an inventory storage center with a constant capacity for each. Each loading job decreases the inventory level of a particular product type and has a predetermined due date, while each unloading job increases the inventory level of a product type and has a given release date. An inbound truck delivers a set of products, which have the same release dates and must be unloaded, to the inventory storage center. In contrast, an outbound truck conveys a set of goods, which have identical completion times and must be loaded. We aim to minimize the total freight cost of trucks as well as the total weighted tardiness of products. To this end, we develop a linear integer programming model and a variable neighborhood search algorithm including a set of efficient local search procedures. Moreover, we run the two previously developed metaheuristics, i.e. a genetic algorithm and a particle swarm algorithm so as to solve the problem. Using a set of randomly generated test instances, we perform extensive computational experiments and statistical analyses to highlight the efficiency and superiority of the developed algorithm.

FIRMACA-Fuzzy intelligent recommendation model using ant clustering algorithm for social networking

Error rate is a challenging parameter to be met for most of the recommendation systems where there is a high probability of item movement among the data clusters. In social networking applications, it is often necessary to produce apt user recommendations where ant-based clustering techniques provide best optimal solutions to the clustering problems. However, the existing ant clustering algorithms lack in efficient local search procedures. Also, they are in need of intelligent fuzzy rule improvements for effective cluster partitioning. Therefore, a new model named Fuzzy Intelligent Recommendation Model using Ant Clustering Algorithm (FIRMACA) is proposed in this paper where a combination of biased exploration and fuzzy rules is used for ant clustering. Experimental analysis shows improvement in recommendation metrics—precision, recall, normalized discounted cumulative gain (NDCG) (≤ 5%) and significant reduction (≤ 1%) in misclassification error rate (MER) compared to contemporary ACO-based algorithms. The selected clusters are optimized globally and locally to pull out the best possible redefined clusters.

Bi-objective optimisation approaches to Job-shop problem with power requirements

Nowadays, a large focus is given to mass personalisation, and multiple path shop floors are suited to such production environments. Hence, this paper deals with the Job-shop scheduling problem that is used for modelling a manufacturing system. Meanwhile, a large attention is given to energy consumption of production systems, but few works consider power requirements of the production systems in order to process operations. In order to contribute in filling this gap, this paper considers the problem where the objective is to minimise both the total completion time of all operations and the instant available power required to process these operations. The problem results in the Bi-objective Job-shop Problem with Power Requirements (Bi-JSPPR). The goal of this paper is to provide a Pareto frontier of schedules minimising both criteria, considering that operations may consume a lot of power at the beginning of the process (consumption peak), more than its consumption after a while, which allows to model power profiles of manufacturing operations. To solve the problem two metaheuristic approaches are investigated: a hybrid Non-dominated Sorting Genetic Algorithm (NSGA-II) and an iterated Greedy Randomized Adaptive Search Procedure coupled with an Evolutionary Local Search (iGRASP×ELS). An efficient local search procedure is specifically designed to improve the quality of solutions in the Pareto frontier of the hybrid NSGA-II (hNSGA-II). Computational experiments and statistical tests are conducted to demonstrate the efficiency of the approaches. Results show that both approach are complementary, having the hNSGA-II showing better average performances, while the iGRASP×ELS is better when high peak power consumption are considered.

Efficient local search procedures for quadratic fractional programming problems

The problem of minimizing the sum of a convex quadratic function and the ratio of two quadratic functions can be reformulated as a Celis–Dennis–Tapia (CDT) problem and, thus, according to some recent results, can be polynomially solved. However, the degree of the known polynomial approaches for these problems is fairly large and that justifies the search for efficient local search procedures. In this paper the CDT reformulation of the problem is exploited to define a local search algorithm. On the theoretical side, its convergence to a stationary point is proved. On the practical side it is shown, through different numerical experiments, that the main cost of the algorithm is a single Schur decomposition to be performed during the initialization phase. The theoretical and practical results for this algorithm are further strengthened in a special case.

A two‐phase Pareto local search heuristic for the bi‐objective pollution‐routing problem

This article deals with the bi‐objective pollution‐routing problem (bPRP), a vehicle routing variant that arises in the context of green logistics. The two conflicting objectives considered are the minimization of the CO2 emissions and the costs related to driver's wages. A multi‐objective approach based on the two‐phase Pareto local search heuristic is employed to generate a good approximation of the Pareto front. During the first phase of the method, a first set of potentially efficient solutions is obtained by solving a series of weighted sum problems with an efficient heuristic originally developed to solve the single‐objective PRP. A dichotomous scheme is used to generate the different weight sets in an automatic way. In the second phase, the set is improved with an efficient Pareto local search (PLS) procedure. The use of PLS allows to limit the number of computational demanding weighted sum problems solved in the first phase, while keeping high‐quality results. Extensive computational experiments over existing benchmark instances show that the proposed approach leads to better results in less CPU time when compared to those obtained by state‐of‐the‐art methods.

Multi-objective retrospective optimization using stochastic zigzag search

We propose a new retrospective optimization (RO) method for multi-objective simulation optimization (MOSO) problems. RO algorithms generate a sequence of sample-path (SP) problems and solve these SP problems iteratively using a nonlinear optimizer. In this study, a stochastic zigzag search algorithm is chosen in the RO framework to solve SP problems. The key idea of zigzag search is searching around the Pareto front by applying an efficient local-search procedure using the gradients of the objective functions. Many continuous MOSO problems have smooth objective functions and their non-dominated objective function values form a smooth surface in the image space. This fact motivates developing the zigzag search method embedded in RO for such relatively well-posed MOSO problems. A numerical implementation of this method—multi-objective retrospective optimization using zigzag search (MOROZS)—is presented particularly for continuous bi-objective simulation optimization (BOSO) problems with well-connected Pareto optimal solutions. MOROZS is designed for BOSO problems in which a simulation oracle returns both objective function values and gradients. Due to the local nature of zigzag search, MOROZS can only guarantee the asymptotic convergence to local Pareto optimality. The efficiency of MOROZS is studied using three BOSO problems with noisy objective functions and is compared to that of Genetic Algorithms based NSGA-II and a recently developed method MO-COMPASS.

Managing multi-line power congestion by using Hybrid Nelder–Mead – Fuzzy Adaptive Particle Swarm Optimization (HNM-FAPSO)

This paper presents a Hybrid Nelder–Mead – Fuzzy Adaptive Particle Swarm Optimization (HNM-FAPSO) for a Multi-Line Congestion Management (MLCM) problem. MLCM is a nonlinear optimization problem in deregulated power system. The generators which are sensitive to the congested lines are selected based on the novel Apparent Power Sensitivity Factor (APSF) and are rescheduled by using the HNM-FAPSO algorithm. The objective of hybridizing the Nelder–Mead (NM), Fuzzy adaptive Particle Swarm Optimization (FAPSO) is to blend their unique advantages as well as their efficacy. The NM method is a very efficient local search procedure and is used to initialize the population for Particle Swarm Optimization (PSO) which is used to search global best value. But PSO has a problem of premature convergence due to linear variation of its internal parameter i.e. inertia weight. To overcome this, a fuzzy inference system is used to dynamically update the inertia weight. The feasibility and performance of the HNM-FAPSO algorithm is demonstrated on the standard IEEE 30-bus system and IEEE 118-bus system. A comparison of simulation results and statistical analysis reveal optimization efficacy of the HNM-FAPSO algorithm over other algorithms like FAPSO, NM, Simple Bacterial Foraging (SBF), adaptive bacterial foraging algorithm with Nelder–Mead (ABFNM), Genetic Algorithm (GA) and PSO available in literature. The main outcome of the proposed algorithm in solving MLCM is reduction in congestion cost, rescheduled real power, power loss and computational time.

Hybridizing mesh adaptive search algorithm and artificial immune systems for discrete rational Bézier curve approximation

This paper is an extension of a previous one presented at the conference Cyberworlds 2014. In that work we addressed the problem of obtaining the rational Bezier curve that fits a given set of data points better in the least-squares sense. Our approach was based on the clonal selection theory principles to compute all parameters of the problem, namely, the control points of the approximating curve, their corresponding weights, and a suitable parameterization of data points. Although we were able to obtain results with good accuracy, this scheme can still be significantly improved by hybridizing it with an efficient local search procedure. This is the approach proposed in this paper. In particular, we consider the mesh adaptive search algorithm, a direct search method aimed at improving the local search step to refine the quality of the solution. This hybrid strategy has been applied to six illustrative free-form shapes exhibiting challenging features, including the three examples in previous paper. A comparative analysis of our results with respect to the previous methodology is also reported. Our experimental results show that this hybrid scheme performs extremely well. It also outperforms the previous approach for all instances in our benchmark.

P-MEMPSODE: Parallel and irregular memetic global optimization

A parallel memetic global optimization algorithm suitable for shared memory multicore systems is proposed and analyzed. The considered algorithm combines two well-known and widely used population-based stochastic algorithms, namely Particle Swarm Optimization and Differential Evolution, with two efficient and parallelizable local search procedures. The sequential version of the algorithm was first introduced as MEMPSODE (MEMetic Particle Swarm Optimization and Differential Evolution) and published in the CPC program library. We exploit the inherent and highly irregular parallelism of the memetic global optimization algorithm by means of a dynamic and multilevel approach based on the OpenMP tasking model. In our case, tasks correspond to local optimization procedures or simple function evaluations. Parallelization occurs at each iteration step of the memetic algorithm without affecting its searching efficiency. The proposed implementation, for the same random seed, reaches the same solution irrespectively of being executed sequentially or in parallel. Extensive experimental evaluation has been performed in order to illustrate the speedup achieved on a shared-memory multicore server. Program summaryProgram title: p-MEMPSODECatalogue identifier: AEXJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9950No. of bytes in distributed program, including test data, etc.: 141503Distribution format: tar.gzProgramming language: ANSI C.Computer: Workstation.Operating system: Developed under the Linux operating system using the GNU compilers v.4.4.3 (or higher). Uses the OpenMP API and runtime system.RAM: The code uses O(n×N) internal storage, n being the dimension of the problem and N the maximum population size. The required memory is dynamically allocated.Word size: 64Classification: 4.9.Nature of problem: Numerical global optimization of real valued functions is an indispensable methodology for solving a multitude of problems in science and engineering. Many problems exhibit a number of local and/or global minimizers, expensive function evaluations or require real-time response. In addition, discontinuities of the objective function, non-smooth and deceitful landscapes constitute challenging obstacles for most optimization algorithms.Solution method: We implement a memetic global optimization algorithm that combines stochastic, population-based methods with deterministic local search procedures. More specifically, the Unified Particle Swarm Optimization and the Differential Evolution algorithms are harnessed with the derivative-free Torczon’s Multi-Directional Search and the gradient-based BFGS method. The produced hybrid algorithms possess inherent parallelism that is exploited efficiently by means of the OpenMP tasking model. Given the same random seed, the proposed implementation reaches the same solution irrespective of being executed sequentially or in parallel.Restrictions: The current version of the software uses only double precision arithmetic. An OpenMP-enabled (version 3.0 or higher) compiler is required.Unusual features: The software requires bound constraints on the optimization variables.Running time: The running time depends on the complexity of the objective function (and its derivatives if used) as well as on the number of available cores. Extensive experimental results demonstrate that the speedup closely approximates ideal values.

An efficient variable neighborhood search for solving a robust dynamic facility location problem in emergency service network

In this study, we propose a robust variant of a dynamic facility location problem that arises from optimizing the emergency service network of Police Special Forces Units (PSFUs) in the Republic of Serbia. We present for the first time a mathematical programming formulation of the problem under consideration. We further propose a Variable Neighborhood Search (VNS) method with an efficient local search procedure for solving real-life problem instances that remained out of reach of CPLEX solver. The results presented in this paper may help in optimizing the network of PSFUs and other security networks as well.

Electromagnetism-like algorithm for support vector machine parameter tuning

This paper introduces an electromagnetism-like (EM) approach for solving the problem of parameter tuning in the support vector machine (SVM). The proposed method is used to tune binary SVM classifiers in single and multiple kernel mode. The internal kernel structure is based on linear and radial basis functions (RBF). An appropriate encoding scheme of EM enables easy transformation of real-valued EM points directly to real-valued parameter combinations. Estimations of the generalization error based on the cross-validation and validation set error are used as objective functions. The efficient local search procedure uses variable size interval movement in order to improve the convergence of the method. The quality of the proposed method is tested on four collections of testing benchmarks through five separate experiments. The first three collections consist of small-size to medium-size classification data sets with up to 60 features and 1,300 training vectors, while the fourth collection is formed of large heterogeneous data sets with up to 1,554 features and 2,186 training vectors. The obtained results indicate that EM outperforms the comparison algorithms in 10 out of 13 instances from the first collection, 5 out of 5 instances from the second, and 13 out of 15 instances from the third collection. The last two experiments, conducted on the fourth collection, show that the proposed method outperforms 14 successful methods in 3 out of 5 data sets where RBF multiple kernel learning is used, and behaves competitively in cases when linear kernels are used.

Zigzag Search for Continuous Multiobjective Optimization

A new method is proposed using a gradient-based zigzag search approach for multiobjective optimization (MOO) or vector optimization problems. The key idea of this method is searching around the Pareto front by applying an efficient local search procedure using the gradients of the objective functions. This local search zigzags along the Pareto surface guided by the gradients and iteratively returns the visited Pareto optima. Many continuous MOO problems have smooth objective functions and the set of the nondominated objective function values forms a regular surface in the image space. This fact motivates developing the zigzag search method for such relatively well-posed MOO problems. A simple implementation of this method, z-algorithm, is presented particularly for continuous bi-objective optimization (BOO) problems with well-connected Pareto optimal solutions. The efficiency of the z-algorithm is studied with a set of BOO problems and the algorithm performances are compared to those of a recently developed MOO algorithm, Pareto front approximation with adaptive weighted sum method.

Optimal power flow under both normal and contingent operation conditions using the hybrid fuzzy particle swarm optimisation and Nelder–Mead algorithm (HFPSO–NM)

In this paper, we solve the optimal power flow problem using by the new hybrid fuzzy particle swarm optimisation and Nelder–Mead (NM) algorithm (HFPSO–NM). The goal of combining the NM simplex method and the particle swarm optimisation (PSO) method is to integrate their advantages and avoid their disadvantages. The NM simplex method is a very efficient local search procedure, but its convergence is extremely sensitive to the selected starting point. In addition, PSO belongs to the class of global search procedures, but it requires significant computational effort. In the other side, in the PSO algorithm, two variables (Φ1,Φ2) are traditionally constant; in this case, due to the importance of these two factors, we decided to obtain these two as fuzzy parameters. The proposed method is firstly examined on some benchmark mathematical functions. Then, it is tested an IEEE 30-bus standard test system by considering different objective functions for normal and contingency conditions to solve optimal power flow. The simulation results indicate that the FPSO–NM algorithm is effective in solving the mathematical functions and the OPF problem.

A Variable Neighborhood Search Approach for Solving the Maximum Set Splitting Problem

This paper presents a Variable neighbourhood search (VNS) approach for solving the Maximum Set Splitting Problem (MSSP). The algorithm forms a system of neighborhoods based on changing the component for an increasing number of elements. An efficient local search procedure swaps the components of pairs of elements and yields a relatively short running time. Numerical experiments are performed on the instances known in the literature: minimum hitting set and Steiner triple systems. Computational results show that the proposed VNS achieves all optimal or best known solutions in short times. The experiments indicate that the VNS compares favorably with other methods previously used for solving the MSSP. ACM Computing Classification System (1998): I.2.8.