Hybrid Scatter Search Research Articles

Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach

Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach

A hybrid scatter search method for solving fuzzy no-wait flow-shop scheduling problems

The literature published since the year 2000 was reviewed regarding the no-wait flow-shop scheduling (No-WFSS) problem. The No-WFSS problem with separate set-up times and fuzzy due dates is addressed to maximize the customer satisfaction index. A scatter search algorithm (SSA) is proposed, hybridized by some operators. The proposed SSA was first used for solving the considered fuzzy no-wait flow-shop scheduling with set-up time (FNo-WFSSWST) problem. Parameters were calibrated using 192 No-WFSS benchmark instances. The proposed SSA was compared with the genetic heuristic, adaptive learning approach, and hybrid ant colony optimization methods from the literature, showing significant performance improvements. It is concluded that the proposed algorithm is an efficient method for solving FNo-WFSSWST problems.

Bi-level programming and multi-objective optimization for the distribution of resources in hierarchical organizations

The decision regarding the hierarchical distribution of resources is crucial for many organizations that want to allocate such resources efficiently. At the upper level of the hierarchy, a decision-maker may have an objective and a set of feasible solutions partially determined by the lower level. Nevertheless, the upper level can influence but not control the decision-maker at the lower level. Moreover, the objectives of the upper and lower levels are conflicting. Hence, the hierarchical distribution of resources can be formulated as a bi-level programming model. This paper reformulates the hierarchical allocation of resources. The Hooke-Jeeves (HJ) algorithm and the hybrid scatter search–Nelder-Mead (SSNM) method are proposed to solve the newly formulated problem. The problem is also analyzed from a multi-objective perspective to equally prioritize the upper and lower levels while subjecting each to an interdependent set of constraints; a multi-objective scatter search algorithm (MSSA) was developed for that purpose. Tailor-made instances were also designed for the implementation of the developed algorithms. The findings demonstrated that the HJ algorithm provides the best solution according to the upper-level objective function. However, it does not guarantee the best result for the lower level. In comparison, MSSA has a set of best possible solutions for both objectives. The hybrid SSNM method could not match the results provided by the former methods.

New Ant Colony Algorithm for Solving Partial Job Shop Scheduling Problem

Scheduling problems are one of the most researched topics in the field of operational research. Scheduling problem models have evolved and branched because of the wide range of products, standards, and customer requirements. Recently, the partial job shop scheduling problem, which is a general model of shop scheduling problems, has become a new scheduling problem. Operations in this model are partially ordered, and the order varies for each job. Several problems studied independently in the literature, such as the group shop, mixed shop, job shop, and open shop scheduling problems, are considered special cases of the partial shop scheduling model. Because ant algorithms are known in the literature as effective tools for solving combinatorial optimization problems, this study proposed an ant colony (AC) algorithm for solving partial shop problems with an objective function to minimize makespan. The AC method was examined and evaluated on the renowned “Taillerd” benchmark instances. It was then compared with the hybrid scatter search (HSS) and iterated tabu search (ITS) methods. The AC algorithm’s average deviation for 80 instances ranged between 0% and 1.78%. The AC algorithm outperforms the HSS and ITS methods, according to the computational findings; where the average percentage relative deviation for AC is 0.66%, compared with 0.99% for ITS and 10.14% for HSS.

Beklemesiz Akış Tipi Çizelgeleme Problemlerinin Analizi ve Hibrit Dağınık Arama Yöntemi ile Çözümü

Beklemesiz Akış Tipi Çizelgeleme (BATÇ), pratik uygulamalarından dolayı kapsamlı bir araştırma alanıdır. BATÇ problemlerinde işler, makinelerde kesintisiz olarak işlem görmek zorundadır. Bir işin tüm makinelerde işlenme süresi boyunca, makineler bekleyebilir fakat işler kesintisiz olarak işlenmelidir. Amaç ise makinelerin boşta bekleme süresini en aza indirmektir. BATÇ problemlerinin çoğunluğunda toplam gecikmenin ve maksimum tamamlanma zamanının minimizasyonu olmak üzere, iki performans ölçüsü göz önünde bulundurulur. Literatürde, son yirmi beş yılda BATÇ ile ilgili yapılan çalışmalar analiz edilmiştir. BATÇ problemlerinin çözümü ile ilgili geliştirilen kesin ve yaklaşık çözüm veren yöntemler incelenmiştir. Literatürde 1 ve 2 makineli problemler için optimum çözüm veren matematiksel yöntemler bulunurken, 3 ve daha fazla makineli problemler için standart zamanda optimum çözüm veren bir yöntem bulunmamaktadır. Kabul edilebilir bir süre içerisinde m makine içeren problemlere optimum ya da optimuma yakın çözümler üretebilmek için sezgisel ve meta sezgisel yöntemler geliştirilmektedir. Bu çalışmada, BATÇ problemlerinin çözümü için Hibrit Dağınık Arama (HDA) yöntemi önerilmiştir. Önerilen yöntem, literatürde iyi bilinen kıyaslama problemleri yardımı ile test edilmiştir. Elde edilen sonuçlar, Hibrit Uyarlanabilir Öğrenme Yaklaşım (HUÖY) algoritması ve Hibrit Karınca Kolonileri Optimizasyon (HKKO) algoritması ile kıyaslanmıştır. Amaç fonksiyonu olarak maksimum tamamlanma zamanının minimizasyonu seçilmiştir. Elde edilen çözüm sonuçları, önerilen HDA yönteminin BATÇ problemlerinin çözümünde etkili olduğunu göstermiştir.

Three Hybrid Scatter Search Algorithms for Multi-Objective Job Shop Scheduling Problem

The Job Shop Scheduling Problem (JSSP) consists of finding the best scheduling for a set of jobs that should be processed in a specific order using a set of machines. This problem belongs to the NP-hard class problems and has enormous industrial applicability. In the manufacturing area, decision-makers consider several criteria to elaborate their production schedules. These cases are studied in multi-objective optimization. However, few works are addressed from this multi-objective perspective. The literature shows that multi-objective evolutionary algorithms can solve these problems efficiently; nevertheless, multi-objective algorithms have slow convergence to the Pareto optimal front. This paper proposes three multi-objective Scatter Search hybrid algorithms that improve the convergence speed evolving on a reduced set of solutions. These algorithms are: Scatter Search/Local Search (SS/LS), Scatter Search/Chaotic Multi-Objective Threshold Accepting (SS/CMOTA), and Scatter Search/Chaotic Multi-Objective Simulated Annealing (SS/CMOSA). The proposed algorithms are compared with the state-of-the-art algorithms IMOEA/D, CMOSA, and CMOTA, using the MID, Spacing, HV, Spread, and IGD metrics; according to the experimental results, the proposed algorithms achieved the best performance. Notably, they obtained a 47% reduction in the convergence time to reach the optimal Pareto front.

Heterogeneous fleet vehicle scheduling problems for dynamic pickup and delivery problem with time windows in shared logistics platform: formulation, instances and algorithms

ABSTRACT his paper introduces a dynamic pickup and delivery problem with time windows, heterogeneous fleet vehicles, no depot, and dynamic priority (DPDP-TWHVNDDP) in the shared logistics platform. The distinguishing feature of DPDP-TWHVNDDP is that the priority and number of requests and the number and types of vehicles available are dynamic, and that all the requests in a scheduling are not necessarily served to maximize the total profit according to their priorities. A mathematical formulation of maximizing profit dynamic scheduling adapting to dynamic priority is established, and a hybrid scatter search parallel algorithm combined with the genetic algorithm, variable neighborhood search algorithm, and tabu search algorithm is proposed to solve the problem with high quality in a relatively short time. Comparison results of our algorithm against the best-known solutions on the benchmark instances available in the literatures show that our algorithm can improve over 35% (52 out of 146) of the total distance and over 30% (44 out of 146) of the vehicle used. A set of DPDP-TWHVNDDP instances based on extending Li and Lim's benchmark instances are introduced. Experiments on benchmarks and actual datasets show that the proposed hybrid heuristic is effective and efficient especially in large scale datasets.

Hybrid Scatter Search Algorithm for Optimal and Energy-Efficient Steelmaking-Continuous Casting

This article studies a steelmaking-continuous casting (SCC) scheduling problem by considering ladle allocation. It takes technological rules in steel manufacturing and ladle-related constraints into account. A scheduling problem is formulated to determine allocation equipment for jobs, production sequence for jobs processed by the same equipment, and modification operations for empty ladles after their service for jobs. To ensure the fastest production and least energy consumption, we present a mixed integer mathematical programming model with the objectives to minimize the maximum completion time, idle time penalties, and energy consumption penalties related to waiting time. To solve it, we develop a two-stage approach based on a combination of scatter search (SS) and mixed integer programming (MIP). The first stage applies an SS algorithm to determine the assignment and sequence variables for charges. For the obtained solution, we construct a temporal constraint network and establish an MIP model at the second stage. We apply ILOG.CPLEX to solve the model and find the final solution. We analyze and compare the performance of the proposed approach with a hybrid method that combines a genetic algorithm with MIP on instances constructed from a real iron-steel plant. To further verify the effectiveness of the proposed algorithm, we compare its results with optimal solutions of the constraint-relaxed original problem. The experimental results show the effectiveness of the proposed approach in solving the SCC-scheduling problem.

A Hybrid Scatter Search Heuristic Algorithm for Solving Cockpit Crew Rostering

This research introduces the development of Hybrid Scatter Search Heuristic for solving cockpit crew (pilot and co-pilot) rostering problem. This research aims to minimize the deviation of flight hours among the cockpit crew of an airline, Garuda Indonesia Airline, during the one-month planning horizon. The weakness of the existing algorithm used in the airline, which is a trial-and-error algorithm, is that the variation among crew flight times for one month is too significant and the scheduling process takes a quite long time. We tested the performance of our proposed algorithm to that of the existing algorithm. The numerical experiments showed that the proposed algorithm had outperformed the existing algorithm. More specifically, we found some in sensitivity analysis experiments. Our experiment results showed that that the higher the flight time target, the higher the total deviation of flight time. We also conducted several experiments to show the robustness of our proposed algorithm. First, we tested the relationship between the number of pilots who can use their preferences and the total deviation of flight time. We conducted experiments by giving the cockpit crew the opportunity to choose a day off. Finally, we analyzed the results by changing the number of cockpit crew.

A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms

In this paper, a new bi-objective fuzzy portfolio selection model is proposed, for which Sharp ratio (SR) and Value at Risk ratio (VR) of a portfolio are chosen as objectives. SR is an important nonsystematic risk measurement that examines the investment risk by aspiring the diversification of the capital allocation. On the other hand, VR measures the systematic risk, which reduces the largest loss of an investment at a given confidence level. The proposed fuzzy portfolio model assumes both SR and VR as maximization objectives for which the associated fuzzy parameters are considered as triangular fuzzy numbers. The proposed model is solved using multi-objective genetic algorithms, namely multi-objective cellular genetic algorithm (MOCell), archive-based hybrid scatter search (AbYSS), and nondominated sorting genetic algorithm II (NSGA-II). We have used a data set from the Shenzhen Stock Exchange to illustrate the performance of the proposed model and algorithms. Finally, a comparative study in terms of five standard performance metrics is presented, among the MOCell, AbYSS, and NSGA-II algorithms that are mentioned extensively in various research articles to exhibit the best suitable algorithm.

A conceptual comparison of NSGA-II, OMOPSO and AbYss algorithms

The optimisation of multi-objective problems is currently an important area of research and development. The importance gained by this type of problem has given rise to the development of multi-objective metaheuristics to attain solutions for such problems. In this paper, an experimental comparison of non-dominated sorting genetic algorithm-II (NSGA-II), archive-based hybrid scatter search (AbYss), and optimised multi-objective particle swarm optimisation (OMOPSO) using ZDT benchmark, has been done to determine which multi-objective metaheuristic has the best performance with respect to a problem. The results thus obtained are compared and analysed based on three performance metrics namely hypervolume, GD, and IGD that evaluate the dispersion of the solutions on the Pareto front and its proximity to it.

The effect of elite pool in hybrid population-based meta-heuristics for solving combinatorial optimization problems

This work investigates the effect of elite pool that has high-quality and diverse solutions in three hybrid population-based meta-heuristics with an elite pool of a hybrid Elitist-Ant System, a hybrid Big Bang-Big Crunch optimization, and a hybrid scatter search. The purpose of incorporating an elite pool in population-based meta-heuristics is to maintain the diversity of the search while exploiting the solution space as in the reference set of the scatter search. This may guarantee the effectiveness and efficiency of the search, which could enhance the performance of the algorithms and generalized well across different datasets. To test the generality of these meta-heuristics via their consistency and efficiency, we use three classes of well-known combinatorial optimization problems as follows: symmetric traveling salesman problem, 0–1 multidimensional knapsack problem, and capacitated vehicle routing problem. Experimental results showed that the performance of our hybrid population-based meta-heuristics, compared to the best known results, is competitive in many instances. This finding indicates the effectiveness of utilizing an elite pool in our hybrid meta-heuristics in diversifying the search and subsequently enhances their performance over different instances and problems.

A DE-Based Scatter Search for Global Optimization Problems

This paper proposes a hybrid scatter search (SS) algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE) into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE) algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.

An Evolutionary Hybrid Algorithm for Layout Planning in Flexible Manufacturing System

The layout of a flexible manufacturing system (FMS) involves distributing different resources for achieving maximum efficiency. To provide a variety of products to customers the FMS has created a significant set of operational changes. Among this, layout planning is more important in achieving productivity of FMS. The problem of this type is combinatorial in nature and found to be Non-deterministic Polynomial (NP) complete. This paper focuses the loop layout planning of an FMS with the aim of minimizing the transportation distance and the backtracking distances of the Automated Guided Vehicles (AGV) using the hybrid Scatter Search - Particle Swarm Optimization algorithm (SS-PSO). Since the Loop layout has relatively low initial costs and contains few material handling links with higher flexibility. SS-PSO operates on unifying principles based on strategic designs compared to other metaheuristic algorithms such as GA, PSO etc. Hybrid SS-PSO approach is applied to seven and nine machines loop layout problem. It is found that the proposed algorithm provides a better solution with fast convergence rate compared with other metaheuristic algorithms.

ASMiGA: an archive-based steady-state micro genetic algorithm.

We propose a new archive-based steady-state micro genetic algorithm (ASMiGA). In this context, a new archive maintenance strategy is proposed, which maintains a set of nondominated solutions in the archive unless the archive size falls below a minimum allowable size. It makes the archive size adaptive and dynamic. We have proposed a new environmental selection strategy and a new mating selection strategy. The environmental selection strategy reduces the exploration in less probable objective spaces. The mating selection increases searching in more probable search regions by enhancing the exploitation of existing solutions. A new crossover strategy DE-3 is proposed here. ASMiGA is compared with five well-known multiobjective optimization algorithms of different types-generational evolutionary algorithms (SPEA2 and NSGA-II), archive-based hybrid scatter search, decomposition-based evolutionary approach, and archive-based micro genetic algorithm. For comparison purposes, four performance measures (HV, GD, IGD, and GS) are used on 33 test problems, of which seven problems are constrained. The proposed algorithm outperforms the other five algorithms.

Enhancing the performance of hybrid genetic algorithms by differential improvement

A differential improvement modification to Hybrid Genetic Algorithms is proposed. The general idea is to perform more extensive improvement algorithms on higher quality solutions. Our proposed Differential Improvement (DI) approach is of rather general character. It can be implemented in many different ways. The paradigm remains invariant and can be easily applied to a wider class of optimization problems. Moreover, the DI framework can also be used within other Hybrid metaheuristics like Hybrid Scatter Search algorithms, Particle Swarm Optimization, or Bee Colony Optimization techniques.Extensive experiments show that the new approach enables to improve significantly the performance of Hybrid Genetic Algorithms without adding extra computer time. Additional experiments investigated the trade-off between the number of generations and the number of iterations of the improvement algorithm. These experiments yielded six new best known solutions to benchmark quadratic assignment problems. Many other variants of the proposed algorithm are suggested for future research.

Adaptive multi-objective archive-based hybrid scatter search for segmentation in lung computed tomography imaging

This article proposes a multi-objective clustering ensemble method for medical image segmentation. The proposed method is called adaptive multi-objective archive-based hybrid scatter search (AMAHSS). It utilizes fuzzy clustering with optimization of three fitness functions: global fuzzy compactness of the clusters, fuzzy separation and symmetry distance-based cluster validity index. The AMAHSS enables the search strategy to explore intensively the search space with high-quality solutions and to move to unexplored search space when necessary. The best single solution is processed using the metaclustering algorithm. The proposed framework is designed to segment lung computed tomography images for candidate nodule detection. This candidate nodule will then be classified as cancerous or non-cancerous. The authors validate the method with standard k-means, fuzzy c-means and the multi-objective genetic algorithm with different postprocessing methods for the final solution. The results obtained from the benchmark experiment indicate that the method achieves up to 90% of the positive predictive rate.

Mathematical Model and Hybrid Scatter Search for Cost Driven Job-shop Scheduling Problem

Job-shop scheduling problem (JSP) is one of the most well-known machine scheduling problems and one of the strongly NP-hard combinatorial optimization problems. Cost optimization is an attractive and critical research and development area for both academic and industrial societies. This paper presents a cost driven model of the job-shop scheduling problem in which the solutions are driven by business inputs, such as the cost of the product transitions, revenue loss due to the machine idle time and earliness/tardiness penalty. And then, a new hybrid scatter search algorithm is proposed to solve the cost driven job-shop scheduling problem by introducing the simulated annealing (SA) into the improvement method of scatter search (SS). In order to illustrate the effectiveness of the hybrid method, some test problems are generated, and the performance of the proposed method is compared with other evolutionary algorithms such as genetic algorithm and simulated annealing. The experimental simulation tests show that the hybrid method is quite effective at solving the cost driven job-shop scheduling problem.

A comparative study of the multi-objective optimization algorithms for coal-fired boilers

Combustion optimization has been proved to be an effective way to reduce the NOx emissions and unburned carbon in fly ash by carefully setting the operational parameters of boilers. However, there is a trade-off relationship between NOx emissions and the boiler economy, which could be expressed by Pareto solutions. The aim of this work is to achieve multi-objective optimization of the coal-fired boiler to obtain well distributed Pareto solutions. In this study, support vector regression (SVR) was employed to build NOx emissions and carbon burnout models. Thereafter, the improved Strength Pareto Evolutionary Algorithm (SPEA2), the new Multi-Objective Particle Swarm Optimizer (OMOPSO), the Archive-Based hYbrid Scatter Search method (AbYSS), and the cellular genetic algorithm for multi-objective optimization (MOCell) were used for this purpose. The results show that the hybrid algorithms by combining SVR can obtain well distributed Pareto solutions for multi-objective optimization of the boiler. Comparison of various algorithms shows MOCell overwhelms the others in terms of the quality of solutions and convergence rate.

A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems

This paper investigates the first hybrid scatter search and path relinking meta-heuristic for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. The underpinning mathematic model of the DCLC multicast routing problem is the constrained Steiner tree problem in graphs, a well known NP-complete problem. After combining a path relinking method as the solution combination method in scatter search, we further explore two improvement strategies: tabu search and variable neighborhood search, to intensify the search in the hybrid scatter search algorithm. A large number of simulations on some benchmark instances from the OR-library and a group of random graphs of different characteristics demonstrate that the improvement strategy greatly affects the performance of the proposed scatter search algorithm. The hybrid scatter search algorithm intensified by a variable neighborhood descent search is highly efficient in solving the DCLC multicast routing problem in comparison with other algorithms and heuristics in the literature.