Local Search Strategy Research Articles

The Hot Strip Mill Scheduling Problem With Uncertainty: Robust Optimization Models and Solution Approaches.

In this article, we focus on a biobjective hot strip mill (HSM) scheduling problem arising in the steel industry. Besides the conventional objective regarding penalty costs, we have also considered minimizing the total starting times of rolling operations in order to reduce the energy consumption for slab reheating. The problem is complicated by the inevitable uncertainty in rolling processing times, which means deterministic scheduling models will be ineffective. To obtain robust production schedules with satisfactory performance under all possible conditions, we apply the robust optimization (RO) approach to model and solve the scheduling problem. First, an RO model and an equivalent mixed-integer linear programming model are constructed to describe the HSM scheduling problem with uncertainty. Then, we devise an improved Benders' decomposition algorithm to solve the RO model and obtain exactly optimal solutions. Next, for coping with large-sized instances, a multiobjective particle swarm optimization algorithm with an embedded local search strategy is proposed to handle the biobjective scheduling problem and find the set of Pareto-optimal solutions. Finally, we conduct extensive computational tests to verify the proposed algorithms. Results show that the exact algorithm is effective for relatively small instances and the metaheuristic algorithm can achieve satisfactory solution quality for both small- and large-sized instances of the problem.

Energy optimization routing for hierarchical cluster based WSN using artificial bee colony

Technology advancement in Wireless sensor network (WSNs) has attracted much attention in smart computing and potential usage across numerous applications fields. WSN composed of tiny and self-configured sensor nodes with battery operated. Sensors are restricted to limited energy and resources. Unbalanced nodes energy results in more energy consumption and affects network lifetime. Achieving energy efficiency remains a challenging issue in designing WSN routing. Approaches for minimising node energy usage through clustering techniques have offered optimal solutions. However, the existing clustering scheme fails to balance nodes energy without considering energy parameters, low energy node being chosen as cluster head, node density, and scalability. Existing scheme limits to global exploration possibilities and restricted to only specific search regions. In this paper, we propose an energy optimization routing using improved artificial bee colony (EOR-iABC) for cluster based WSN. The proposed EOR-iABC routing scheme intends to achieve energy optimization and prolong network's lifetime. The EOR-iABC adapts distinctive search policy using improved artificial bee colony algorithm for selection of energy efficient cluster heads (CH) in periodic time intervals through integration of crossover and mutation. The delay convergence is eliminated by associating employee and onlooker-bee stages, which helps to reform local search strategies. An optimal path from CH to base station (BS) is discovered through energy-efficient fitness node to improve network data collection efficiency. Grenade explosion method (GEM) and Cauchy operator are employed to extend search policies dynamically from one region to another for large-scale WSN. Simulation results show EOR-iABC outperforms in terms of energy efficiency by 27% compared to OCABC scheme and by 16% compared to IABCOCT scheme.

Analysis of the influence of population distribution characteristics on swarm intelligence optimization algorithms

The distribution characteristic of populations is one of the main characteristics of population. The pattern of distribution characteristics determines the probability law of individual values. At the same time, the initialization of the population lays a foundation for the iterative process of the swarm intelligence optimization algorithm. To reveal the influence of population distribution characteristics on the swarm intelligence optimization algorithm, this paper proposes a variety of search strategies based on the populations with different distribution characteristics and analyzes the influence of population distribution characteristics on optimization process by comparing the test results of the optimization algorithm after implementing these strategies. First, a new population generator is designed that can transform the same initial population into a population with uniform and central peaking distributions. On this basis, the two kinds of populations are applied to the global and local search stages of the optimization process, and four different search strategies are formed. Among them, the global and local search strategies based on a uniformly distributed population are the traditional methods. Finally, the performance of the optimization algorithm using different search strategies is evaluated through 29 test problems from the CEC2017 benchmark for 10, 30, 50 and 100 dimensions. In addition, the algorithms are applied to solve the TSP problem. For CEC2017 in 100D, only 13 of the 29 test functions achieve the best optimization effect by using the traditional method, while the other 16 test functions achieve better search results by using the other three search strategies. The analysis shows that the population distribution characteristics have a great influence on the population optimization algorithm. The performance of the algorithm with different population distribution combination strategies is statistically superior to the traditional algorithm with a uniform distribution population, as revealed in the test functions ranging from 38.7% to 62.9% for different dimensions. By reconstructing populations with different distribution characteristics, the overall efficiency of the swarm intelligence optimization algorithm can be greatly improved.

A binary chaotic horse herd optimization algorithm for feature selection

One of the most challenging and common problems in machine learning is the Feature Selection (FS) process, which reduces the dataset size by finding optimal subsets of features. The Horse Herd Optimization Algorithm (HOA) is a new metaheuristic algorithm created by modeling the herd behavior of horses and developed for large scale optimization problems. This paper proposes the binary version of the HOA as a wrapper FS method to solve the FS problem. The proposed algorithm is a binary chaotic horse herd optimization algorithm for feature selection (BCHOAFS). The proposed BCHOAFS is applied to select the optimal feature combination that maximizes classification accuracy while minimizing the number of selected features. Classifier algorithms from machine learning algorithms were used to test the accuracy of the reduced subsets. The proposed method was named binary horse herd optimization for feature selection (BHOAFS) before adding chaotic maps; the k-nearest neighbor (k-NN) and Support Vector Machine (SVM) were tested as separate classifiers. It has been seen that k-NN classification accuracy gives better results than SVM. The BHOAFS-kNN method using the k-NN classification was combined with five chaotic maps and named as BCHOAFS-Logistics, BCHOAFS-Piecewise, BCHOAFS-Singer, BCHOAFS-Sinusoidal, BCHOAFS-Tent. The BCHOAFS versions were run on datasets consisting of 18 different sizes and quality datasets (i.e., low scale, medium scale, and large scale) taken from the UCI repository and compared with state-of-the-art algorithms in previous studies. The results prove that the proposed version, especially with the BCHOAFS-Piecewise and the BCHOAFS-Singer chaotic map outperforms or competes with well-known methods. The proof of the proposed approach’s statistical significance has been validated using the Friedman Signed Rank test and post hoc Wilcoxon test. The novelty of BCHOAFS is that HOA, which is an optimization algorithm specially designed for large scale data, is the first binary chaotic-based algorithm developed for feature selection problems. It also proposes a new local search strategy called Similarity Measurement Function (SMF). As a result, versions of the proposed algorithm BCHOAFS can be used for the FS problem.

Sepsis Prediction by Using a Hybrid Metaheuristic Algorithm: A Novel Approach for Optimizing Deep Neural Networks.

The early diagnosis of sepsis reduces the risk of the patient's death. Gradient-based algorithms are applied to the neural network models used in the estimation of sepsis in the literature. However, these algorithms become stuck at the local minimum in solution space. In recent years, swarm intelligence and an evolutionary approach have shown proper results. In this study, a novel hybrid metaheuristic algorithm was proposed for optimization with regard to the weights of the deep neural network and applied for the early diagnosis of sepsis. The proposed algorithm aims to reach the global minimum with a local search strategy capable of exploring and exploiting particles in Particle Swarm Optimization (PSO) and using the mental search operator of the Human Mental Search algorithm (HMS). The benchmark functions utilized to compare the performance of HMS, PSO, and HMS-PSO revealed that the proposed approach is more reliable, durable, and adjustable than other applied algorithms. HMS-PSO is integrated with a deep neural network (HMS-PSO-DNN). The study focused on predicting sepsis with HMS-PSO-DNN, utilizing a dataset of 640 patients aged 18 to 60. The HMS-PSO-DNN model gave a better mean squared error (MSE) result than other algorithms in terms of accuracy, robustness, and performance. We obtained the MSE value of 0.22 with 30 independent runs.

Backtracking search optimization algorithm with dual scatter search strategy for automated test case generation

It is a challenge to design an effective algorithm utilizing problem features in automated test case generation for path coverage (ATCG-PC). A feature of ATCG-PC “similar paths are usually executed by similar test cases” was touched by a few scholars and can be further exploited to design more effective algorithms. Inspired by this feature, this paper proposes a two-stage local search strategy, denoted dual scatter search (DS) strategy, which concatenates two improved scatter search strategies with different search behaviors. The first stage aims to fully exploit the discovered test cases to search for desired test cases, and the latter stage aims to mine the unexploited areas of the first stage via using less computational overhead. Then, a backtracking search optimization algorithm with dual scatter search strategy (BSA-DS) is proposed, which incorporates DS strategy into the backtracking search optimization algorithm (BSA) with strong exploration capability. BSA is first introduced into the field of ATCG-PC. The performance of BSA-DS and some state-of-the-art algorithms is tested on twelve popular benchmark programs. Experimental studies demonstrate that BSA-DS achieves the highest path coverage with the fewest test cases and running time on at least eight out of the twelve programs.

A Mayfly algorithm for cardinality constrained portfolio optimization

Portfolio optimization is an essential issue in quantitative investing, which aims to find the best set of portfolios by allocating the proportion of assets. One of the most widely studied portfolio optimization models is the cardinality constrained mean–variance model, which incorporates real-world constraints on the number of selected assets and lower and upper bounds on the proportion of each asset. This paper presents a novel metaheuristic algorithm based on the Mayfly algorithm to solve the cardinality constrained mean–variance portfolio optimization problem. To better adapt to this problem, we design and introduce some new features to the proposed algorithm, including (1) a new cardinality constraint handling strategy; (2) a new local search strategy; and (3) changes to the crossover operator. We have designed comparison experiments for the proposed metaheuristic and evaluated its performance using five commonly used performance metrics. The experimental results show that the proposed approach achieves competitive performance on datasets of different sizes. The results also demonstrate the feasibility of this approach in solving the cardinality constrained mean–variance portfolio optimization problem.

Scenario-Based Robust Remanufacturing Scheduling Problem Using Improved Biogeography-Based Optimization Algorithm

As a promising method for organizing remanufacturing production activities, remanufacturing scheduling has attracted increasing attention in recent years. However, extant studies have primarily focused on solving remanufacturing scheduling problems in a deterministic environment, while neglecting the impact of uncertainties on remanufacturing. Therefore, a new scenario-based robust remanufacturing scheduling problem was investigated in this study, and a robust optimization model for this problem was established. In the proposed model, a discrete scenario set is used to describe the uncertain arrival time and uncertain processing time of end-of-life products, and the variable start-up batch size constraint is considered to improve the practicality and flexibility of the model. To solve this model, an improved biogeography-based optimization algorithm with a new three-dimensional unequal-length representation scheme is proposed, in which, new migration and mutation operators, a local search strategy, and a new batch promotion mechanism are designed to improve the algorithmic performance. The results of the experiments demonstrate the feasibility of the proposed model and the superiority of the presented algorithm in solving the proposed model.

A new boredom-aware dual-resource constrained flexible job shop scheduling problem using a two-stage multi-objective particle swarm optimization algorithm

Dual-resource constrained flexible job shop scheduling problem has become a hot research field in recent years. However, few studies have considered workers’ boredom sensations when allocating resources and scheduling tasks, leading to inappropriate task allocation and negative effects such as efficiency reductions and absenteeism. Therefore, a new boredom-aware dual-resource constrained flexible job shop scheduling problem is investigated in this study, which considers the increase in workers’ boredom caused by repetitive job assignments and constructs an efficiency function to characterize the impact of workers’ boredom. For this problem, a bi-level lexicographic model, which takes the effective completion of all manufacturing tasks as the primary optimization objective and higher worker job satisfaction as the secondary optimization objective, is established. A two-stage multi-objective particle swarm optimization algorithm with a three-dimensional representation scheme is presented to solve this model. In this algorithm, a new position-updating mechanism and a local search strategy are devised to effectively evolve the solution, and a decomposition strategy with a self-adaptive neighborhood size and a boundary exploration mechanism are embedded to obtain a uniformly distributed Pareto front. Experimental results confirm the superiority of the presented model and algorithm.

A knowledge-driven multiobjective algorithm for distributed hybrid flowshop with group and carryover setup in glass manufacturing systems

The distributed hybrid flow shop problem (DHFSP) exists widely in real workshop production processes. Its process optimization has important academic significance and application value, and has become one of the research hotspots in the field of production scheduling. In this study, a multiobjective DHFS problem with carryover setup time and group constraints (DHFGSP) is considered with the background of glass processing, and the objectives are the completion time and time of use price. First, a mathematical programming model is established according to the processing flow of glass production. Second, an improved nondominated sorting genetic algorithm-II (INSGAII) is adopted to optimize the problem. Third, the evolutionary strategies based on problem knowledge are developed, and a local search strategy based on critical factories is designed. Finally, the proposed algorithm is compared with several of the most advanced multiobjective algorithms, which shows that INSGA-II has better performance for solving DHFGSP.

Effective Feature Selection Strategy for Supervised Classification based on an Improved Binary Aquila Optimization Algorithm

Feature Selection (FS) is considered a crucial step in machine learning and data mining tasks, which facilitates minimizing the direct consequence of redundant and irrelevant attributes on the model’s accuracy. Hence, the researchers developed various algorithms to choose the most appropriate features for improving the accuracy rate of the presented dataset. Nevertheless, these algorithms may fall into local optima problems when applied to substantial feature sizes’ datasets. In this paper, for handling the FS strategy through dimensionality-lessening while improving the classification accuracy, an effective Aquila Optimization (AO) algorithm is introduced. AO has stable exploration and exploitation capabilities. It is enhanced by integrating a random position amendment approach with Local Search (LS) strategy to avoid local optima and then cloned into a binary version called Improved Binary AO (IBAO). Additionally, k-Nearest Neighbor (k-NN) and Support Vector Machine (SVM) are quality estimators. On 18 multi-scale benchmarks, the IBAO algorithm is compared with the original BAO algorithm and twelve recent algorithms, such as Binary Artificial Bee Colony (BABC), Binary Bat Algorithm (BBA), Binary Particle Swarm Optimization (BPSO), Binary Whale Optimization Algorithm (BWOA), Binary Grey Wolf Optimization (BGWO), Binary Sailfish Optimizer (BSFO), Binary Henry Gas Solubility Optimization (BHGSO), Binary Harris Hawks Optimization (BHHO). According to Wilcoxon’s rank-sum test (α=0.05), the dominance and significant influence of IBAO are apparent on both small and large dimensional benchmarks and obtained classification accuracy up to 100% in some of these benchmarks integrated with a feature reduction size down to 92%.

An efficient hybrid optimization method for Fuzzy Flexible Job-Shop Scheduling Problem: Steady-state performance and analysis

Due to the uncertainty pervasive in manufacturing and production systems, a crisp processing time is no longer appropriate. Thus, the flexible job-shop scheduling issue comes with fuzzy processing times. Fuzzy numbers are used to depict the uncertainty associated with processing times. This paper proposes a Hybrid Fuzzy Flexible job-shop Scheduling Approach (HFFSA) for addressing the Fuzzy Flexible Job-Shop Scheduling Problem (FFJSSP). An encoding-and-decoding scheme is employed for initializing the population. HFFSA incorporates four operators to enhance the quality of solutions: the Different Positions Shuffling (DPS) operator, the Randomly Selected Positions Shuffling (RSPS) operator, the Block Shuffling (BS) operator and the Inversion Mutation (IM) operator. The DPS operator shuffles the different positions between a randomly generated solution and the current one. On the other hand, the RSPS shuffles random positions to maintain population diversity. The BS and IM work on a subset of positions from the current solution to obtain near-optimal solutions. Furthermore, we integrate the pair-wise local search strategy with HFFSA to improve the best solution. HFFSA is compared to twenty-five algorithms using Lei and remanufacturing benchmarks. Several statistical measures are employed, like the CPU time, best, average and worst fuzzy makespan values, boxplots and the Wilcoxon signed-rank test. The statistical analyses affirm the superiority of the proposed HFFSA.

A decomposition-based multi-objective Jaya algorithm for lot-streaming job shop scheduling with variable sublots and intermingling setting

This study examined the lot-streaming job shop scheduling problem (LSJSP) with variable sublots and intermingling setting, which has rarely been considered in the literature and is beneficial to real industry settings. Upon variable sublots and intermingling setting, a multi-objective mixed-integer linear programming model (MILP) is formulated to achieve a tradeoff between the shortest tardiness and the minimum number of transferred sublots. Considering the NP-hard characteristic of the problem, the MILP model would get restricted in solving medium and large scale instances. Thus building an efficient multi-objective optimization algorithm is desirable. Motivated by the Jaya algorithm and decomposition idea, we propose a new algorithm framework called a decomposition based multi-objective Jaya algorithm (MOJA/D) to achieve a balance between exploration and exploitation. This MOJA/D framework can provide some guidance in algorithm construction for other multi-objective optimization problems. Following the MOJA/D framework, a specific MOJA/D metaheuristic is further designed for coping with the proposed problem. First, a novel forward and backward decoding strategy is designed to implement coevolution among different sub-problems and enhance the population diversity. Second, the Jaya updating mechanism is designed based on problem knowledge to guide the solutions moving towards the best solution and away from the worst solution. Moreover, considering the tradeoff between two conflicting objectives, the problem-specific local search strategies are designed and integrated with the neighborhood based local search strategies to enhance exploitation in the search process. The influence of parameter setting on MOJA/D is investigated by using design of experiments. The statistical results from extensive computational experiments demonstrate the effectiveness of the specific algorithm designs and show that the MOJA/D metaheuristic is superior to the existing algorithms in solving the proposed problem.

Hospital evacuation in large-scale disasters using limited aerial transport resources

Hospitals play a key role in providing medical assistance in a post-disaster phase. However, depending on the nature, scale, and severity of disasters, they may also be affected and may need to evacuate their patients. Current evacuation response plans for hospitals are predominantly based on the use of land vehicles, whereas little methodological advancements have been reported for when aerial hospital evacuations become necessary. To address this problem, this study develops a model that facilitates evacuation planning for moving patients from at-risk hospitals to remote locations using limited aerial transportation resources. A subset of the model parameters is treated as stochastic in order to reflect the uncertainties involved in real-world emergency conditions. The complexities of the model are handled via the use of a metaheuristic approach, the Variable neighbourhood search (VNS) algorithm, to provide a suitable solution within a reasonable amount of time. A relaxed mathematical model is used in the proposed VNS to generate an initial solution, which is then transformed into a feasible solution through a try-and-error procedure. The proposed method applies a reinforcement learning procedure that uses different local search strategies within the loop of the VNS. A hypothetical evacuation scenario of real-life scale, from an island state in Australia to the mainland states, is used to evaluate the ability of the model to generate efficient plans. In this case study, Tasmania is considered as an evacuation point, while hospitals located in other major cities host evacuated patients. Comparing the proposed method with a conventional method shows superior performance based on all relevant metrics. Emergency response agencies across many countries that can adopt the proposed methodology, when facing large-scale emergencies caused by wars, epidemics, or natural hazards such as wildfires and earthquakes.

A Swarming Meyer Wavelet Computing Approach to Solve the Transport System of Goods

The motive of this work is to provide the numerical performances of the reactive transport model that carries trucks with goods on roads by exploiting the stochastic procedures based on the Meyer wavelet (MW) neural network. An objective function is constructed by using the differential model and its boundary conditions. The optimization of the objective function is performed through the hybridization of the global and local search procedures, i.e., swarming and interior point algorithms. Three different cases of the model have been obtained, and the exactness of the stochastic procedure is observed by using the comparison of the obtained and Adams solutions. The negligible absolute error enhances the exactness of the proposed MW neural networks along with the hybridization of the global and local search schemes. Moreover, statistical interpretations based on different operators, histograms, and boxplots are provided to validate the constancy of the designed stochastic structure.

Evolutionary Multi-Objective Optimization in Searching for Various Antimicrobial Peptides [Feature

Antimicrobial peptides (AMPs), which are parts of the innate immune response found among all classes of life, are promising in broad-spectrum antibiotics and drug-resistant infection treatments. Although AMPs effectively kill bacteria, numerous AMPs widely distributed in the sequence space remain unknown to humans. Therefore, the de novo design of AMPs involves the exploration of vast sequence space to identify peptides with high antimicrobial activity and good diversity among the known AMPs. Computational intelligence approaches have successfully identified some AMPs; however, most of them fail to address the diversity of the obtained AMPs. This paper reports an evolutionary multi-objective approach for AMP design to optimize both the antimicrobial activity and diversity among identified AMPs. Our approach employs a deep learning model to predict a peptide’s antimicrobial activity and a niche sharing method to estimate a peptide’s density. Then, an evolutionary multi-objective algorithm is presented to simultaneously optimize the objectives of antimicrobial activity and diversity. The algorithm takes the advantage of a decomposition-based framework to search for AMPs with good diversity. These AMPs are collected by an elite archive during the evolution process. Moreover, a local search strategy is applied to enhance the quality of the identified AMPs. The experimental results show that the proposed approach outperforms the state-of-the-art designs in searching for various AMPs. The AMPs generated by the proposed approach have high antimicrobial activities and are distinct from each other and among the AMPs in the datasets.

Reusing Delivery Drones for Urban Crowdsensing

Thanks to the increasing number and massive coverage, delivery drones, equipped with various sensors, have demonstrated significant but unexplored potentials for large-scale and low-cost urban sensing during package delivery. In this paper, we propose novel studies on the reutilization of such delivery drone resources to fill this void in urban crowdsensing. Accounting for interdependency between flying/sensing and drone delivery weight, we jointly optimize route selection, sensing time, and delivery weight allocation, to maximize delivery and sensing utility under drones energy constraints. This problem is formulated as a non-convex mixed integer non-Linear programming problem, which is proved to be NP-hard. To address this intricate problem, we propose near-optimal algorithms that leverage the equivalent objective function construction, the local search scheme, and the alternating iteration technique. Theoretical analysis indicates that our algorithms can achieve the 1/(4+ -approximation ratio (where is an arbitrarily small positive parameter and the convergence guarantee in polynomial time, for the scenarios of fixed and adjustable delivery weights, respectively. Extensive trace-based simulations and field experiments demonstrate that ours can significantly improve the delivery & sensing utility by 124.7% and the energy utilization rate by 72.2% on average, compared with the drone delivery without reusing.

Evolutionary Optimization of Energy Consumption and Makespan of Workflow Execution in Clouds

Making sound trade-offs between the energy consumption and the makespan of workflow execution in cloud platforms remains a significant but challenging issue. So far, some works balance workflows’ energy consumption and makespan by adopting multi-objective evolutionary algorithms, but they often regard this as a black-box problem, resulting in the low efficiency of the evolutionary search. To compensate for the shortcomings of existing works, this paper mathematically formulates the cloud workflow scheduling for an infrastructure-as-a-service (IaaS) platform as a multi-objective optimization problem. Then, this paper tailors a knowledge-driven energy- and makespan-aware workflow scheduling algorithm, namely EMWSA. Specifically, a critical task adjustment-based local search strategy is proposed to intelligently adjust some critical tasks to the same resource of their successor tasks, striving to simultaneously reduce workflows’ energy consumption and makespan. Further, an idle gap reuse strategy is proposed to search the optimal energy consumption of each non-critical task without affecting the operation of other tasks, so as to further reduce energy consumption. Finally, in the context of real-world workflows and cloud platforms, we carry out comparative experiments to verify the superiority of the proposed EMWSA by significantly outperforming 4 representative baselines on 19 out of 20 workflow instances.

A hybrid biogeography-based optimization algorithm for three-dimensional bin size designing and packing problem

The three-dimensional bin packing problem (3D-BPP) plays a critical role in logistics activities. Prior studies focus on 3D-BPP in cases where bin size is predetermined. However, bin volume utilization can be improved significantly by optimizing bin size. In this study, we propose a novel three-dimensional bin size designing and packing problem (3D-BSDPP) and a hybrid biogeography-based optimization (HBBO) algorithm to address the problem by maximizing bin volume utilization by optimizing the bin size. The HBBO combines a differential evolution algorithm with basic biogeography-based optimization to improve exploration ability, and a novel local search strategy involving three specific local search operators is proposed to accelerate the HBBO convergence. Finally, a novel heuristic packing method is employed to find a high-quality packing solution. The proposed algorithm is evaluated through experiments carried out on a practical bin packing application. The results indicate that the proposed algorithm outperforms existing algorithms in solving the 3D-BSDPP.

Combining genetic local search into a multi-population Imperialist Competitive Algorithm for the Capacitated Vehicle Routing Problem

The Vehicle Routing Problem (VRP) is one of the most significant problems in operational research today. VRP has a vast range of application fields such as transportation, logistics, manufacturing, relief systems and communication. To suit the needs of different real-world VRP scenarios, many models of VRP have been developed — CVRP (Capacitated VRP) being the classical form. In this article, a hybrid metaheuristic algorithm, ICAHGS, is proposed for solving CVRP. The present study proposes a refined Imperialist Competitive Algorithm (ICA) as the primary evolutionary and multi-population method for addressing the Capacitated Vehicle Routing Problem (CVRP). In order to further optimize the search process, a Hybrid Genetic Search (HGS-CVRP) algorithm is applied as an enhanced local search and population management strategy within the ICA framework. Additionally, the internal restart step of the HGS-CVRP algorithm is replaced with a multi-step restart mechanism for intensification improvement. One notable aspect of the proposed method is its ability to facilitate parallel processing, with each empire able to be processed on a separate processor. This structure allows for increased computational efficiency in addressing the CVRP. To assess the effectiveness of the proposed algorithm, it has been compared to several state-of-the-art algorithms from the literature. The results of this comparison, which include both classical benchmark instances and real-world applications, demonstrate the competitive performance of the proposed algorithm.