Scatter Search Research Articles

A bi-population cooperative scatter search algorithm for distributed hybrid flow shop scheduling with machine breakdown

The occurrence of machine breakdowns is a frequent and dynamic phenomenon in the production process. The implementation of effective preventive measures can mitigate such events and result in reduced production costs. This paper investigates the distributed hybrid flow shop scheduling problem with machine breakdown (DHFSSPB) considering short maintenance time. The bi-population cooperative scatter search (BCSS) algorithm is proposed to address the DHFSSPB, wherein the search for the optimal scheduling sequence is transformed into genetic evolution aiming to obtain a gene chain with both minimum lower bound and minimum cost attributes. Firstly, the DHFSSPB problem is modeled through a combination of predictive maintenance strategy and right-shift rescheduling rule. Subsequently, a diversification approach is developed to facilitate attribute inheritance, enhance the efficiency of job allocation, and establish a reference set. The reference set is partitioned into two subpopulations based on lower bound attributes and cost attributes, respectively. The corresponding hybrid search strategies are designed to enhance the efficiency of job sorting and machine selection for subpopulations with distinct attributes. The cooperative evolution between subpopulations occurs through the competitive interaction and fusion of individuals. An enhanced reinforcement learning approach is proposed to expedite the acceleration of individual attribute evolution by leveraging evolutionary knowledge acquired from populations, thereby effectively guiding the evolutionary trajectories of individuals. Additionally, a method for evaluating the population during the learning process is developed based on problem characteristics to enhance learning efficiency. Experimental results demonstrate that BCSS outperforms the comparative algorithm in solving the DHFSSPB.

Two-stage learning scatter search algorithm for the distributed hybrid flow shop scheduling problem with machine breakdown

The distributed hybrid flow shop scheduling problem with machine breakdown is investigated to reduce the negative impact on real production caused by machine breakdown events. (DHFSPMB). DHFSPMB comprises two subproblems: the maintenance problem with machine breakdown and the distributed hybrid flow shop scheduling problem (DHFSP). A rescheduling method is designed to address the maintenance problem. Subsequently, a two-stage learning scatter search (TLSS) algorithm is proposed for optimizing the DHFSP when the machines break down. Firstly, a mixed integer programming model for DHFSPMB is constructed. Secondly, TLSS employs an improved reinforcement learning approach to enhance the capability of exploration by guiding the direction of global search. A two-stage approach is designed to address the lack of knowledge in the early periods of learning. Finally, a hybrid search strategy is devised to enhance the development capability of TLSS. The experimental results demonstrate that the TLSS algorithm outperforms the comparison algorithms in effectively addressing the DHFSPMB.

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.

Bayesian network structure learning using scatter search

Learning the structure of Bayesian networks (BNs) from data is an NP-hard problem as the solution space grows super-exponentially with the number of nodes. Many algorithms have been developed to efficiently find the best structures, with score-based algorithms being those that use heuristics or metaheuristics to explore potential structures in the search space. This paper proposes a new score-based algorithm that relies on a well-known metaheuristic called scatter search, which, to the best of our knowledge, has not been used in learning BN structure. The core of scatter search is to maintain a reference set that stores both high-quality and diverse solutions, thereby continuously tracking and improving the high-quality solutions, while exploring different search directions indicated by the diverse solutions. By incorporating a distance metric in the learning process, the exploration can be more systematic than purely random, as is often the case in most existing algorithms. The effectiveness and efficiency of the proposed algorithm are evaluated through computational experiments. In addition to learning higher-score structures, the results show that scatter search provides a higher degree of robustness compared with benchmark algorithms.

Joint optimization of inventory replenishment and rationing policies for an omnichannel store with both in-store and online demands

Boosted by the COVID-19 pandemic, omnichannel retail has become a popular retail model and is expected to further grow. We study inventory replenishment and rationing of a product in an omnichannel store that fulfils both in-store and online demands. Both demands follow Poisson process. As each in-store demand must be satisfied immediately whereas each online order has a delivery time window, the two demand classes have different behaviors facing stockout: offline demand is lost while online order is backlogged with backorder cost charged only if it is delivered late. The inventory replenishment and rationing between the two demand classes in this omnichannel inventory system are controlled by a continuous review (Q, r) policy and a critical level policy, respectively. The intertwined nature of inventory replenishment and rationing in this system makes its analytical cost evaluation and its joint optimization of the two policies challenging. After deriving an analytical formula for evaluating the expected cost of the system, two heuristic algorithms are proposed to jointly optimize the two policies. Numerical experiments on randomly generated instances demonstrate that the multi-start local search algorithm and the scatter search algorithm can obtain a near-optimal solution quickly with percentage cost gap no larger than 0.81% and 0.18%, respectively, and the critical level policy can yield cost savings up to 10.91% compared to the first-come, first-served policy. Finally, a sensitivity analysis is conducted to evaluate the influences of system parameters on the optimal critical level.

Scatter search with stochastic beam search on the coalition formation problem

Scatter search with stochastic beam search on the coalition formation problem

Passive filters allocation in unbalanced distribution network with high penetration of distributed generation

The purpose of this paper is the allocation of passive filters in an unbalanced power network with high penetration of distributed generation to minimize the costs of power losses in the distribution lines, including power losses caused by harmonic components and neutral conductor power losses due to unbalanced loads. The harmonic components and the fundamental current generated by the distributed generation cause a voltage increase in the generation bus, and the voltages in the network above the limit allowed by standard are reduced by allocating passive filters without cutting the active power in the distributed generation. The unbalance and reactive power compensation is performed by the ideal compensation method applied to the distribution network. The tests are for the IEEE 34 bus network, with the fourth wire in the simulation being the isolated neutral. The scatter search metaheuristic applied in the simulation tends to minimize the costs of power losses in the lines and the costs of the passive filters allocated in the medium voltage distribution network, meeting the operational constraints of the network.

Specialized scatter search algorithm for optimal transmission switching with voltage control

This article presents a specialized scatter search (SS) algorithm to solve the optimal transmission switching (OTS) problem considering voltage control, with the objective of reducing operational costs. The nonlinear ac operation of the network is considered, and discrete variables are used to represent the states of the lines, positions of the taps of the transformers, and the states of shunt reactive compensators. The resulting formulation is a mixed-integer nonlinear programming problem, which is nonconvex and hard to solve. The proposed SS algorithm manages the discrete variables of the problem, which becomes a nonlinear programming (NLP) problem when the discrete variables are fixed. The NLP problem is then solved by an optimization solver, which returns all other continuous variables of the problem to the SS algorithm. Tests were conducted using eleven benchmark systems. The results indicated that the SS algorithm is efficient for solving the problem.

ESSENT: an arithmetic optimization algorithm with enhanced scatter search strategy for automated test case generation

As one of the main research tasks in software testing, automated test case generation based on path coverage (ATCG-PC) aims to achieve maximum path coverage with a minimized set of test cases. In ATCG-PC, the correlation among the dimensions of test cases is widely utilized in academia to minimize the search efforts of the search-based algorithm. Nevertheless, the information related to target path selection is not utilized, which leads to blind decision-making by the search-based algorithm during the target path selection. Therefore, this paper proposes an enhanced scatter search strategy by using opposition-based learning. An arithmetic optimization algorithm is also proposed to solve ATCG-PC based on the enhanced scatter search strategy, namely, ESSENT. The ESSENT algorithm selects the path with the lowest path entropy among the uncovered paths as the target path, and generates new test cases that cover the target path by modifying the dimensions of the existing test cases. The performance of the ESSENT algorithm is evaluated on six iFogSim subprograms and six Stanford coreNLP subprograms. Experiment results show that the ESSENT algorithm achieves a higher convergence rate than other state-of-the-art algorithms. Furthermore, it enables maximum path coverage with fewer test cases.

Scatter search for capacitated minimum spanning tree

We develop a scatter search algorithm for the classical capacitated minimum spanning tree (CMST) problem. We address both the homogeneous and the more difficult heterogeneous variant of the problem. The CMST is central in a wide range of network design applications in industrial engineering, routing and logistics, and communication networks. Since the problem is NP-Complete, heuristic solution methods are often required to find high-quality solutions within practical time limits. Research efforts have been focused on complex algorithm designs combining advanced neighborhood search techniques with exact solution methods or hybrids of genetic algorithms with various alternative search techniques and likewise supplemented with optimization procedures. In this study we go back to the roots and offer an alternative algorithm that competes with the best algorithms in the literature and both avoids complicated artifacts and is simpler to implement. Key features of the proposed algorithm include an oscillation neighborhood search method characterized by two classes of neighborhoods and an evolutionary search procedure based on a scatter search framework.

ALGORITMO DE BUSCA DISPERSA PARA RESOLUÇÃO DE PROBLEMAS DE OTIMIZAÇÃO DISCRETOS E CONTÍNUOS

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

Solving a Two-Level Location Problem with Nonlinear Costs and Limited Capacity: Application of Two-Phase Recursive Algorithm Based on Scatter Search

Abstract This study examines the issue of distribution network design in the supply chain system. There are many production factories and distribution warehouses in this issue. The most efficient strategy for distributing the product from the factory to the warehouse and from the warehouse to the customer is determined by solving this model. This model combines location problems with and without capacity limits to study a particular location problem. In this system, the cost of production and maintenance of the product in the factory and warehouse is a function of its output. This increases capacity without additional costs, and ultimately does not lose customers. This algorithm is a population-based, innovative method that systematically combines answers to obtain the most accurate answer considering quality and diversity. A two-phase recursive algorithm based on a scattered object has been developed to solve this model. Numerical results show the efficiency and effectiveness of this two-phase algorithm for problems of different sizes.

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.

A Cooperative Scatter Search With Reinforcement Learning Mechanism for the Distributed Permutation Flowshop Scheduling Problem With Sequence-Dependent Setup Times

The integration of reinforcement learning technology into meta-heuristic algorithms to address complex combinatorial optimization problems has attracted much attention in recent years. A cooperative scatter search with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning mechanism (QCSS) is proposed for solving the DPFSP-SDST. In the diversification generation method, two effective heuristic algorithms are designed to construct an initial population with high quality and diversity. In the improved method, eight domain knowledge-guided perturbation operators are combined with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning to balance the exploration and exploitation capabilities of the QCSS algorithm. The reference set <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathrm{RefSet})$</tex-math> </inline-formula> is divided into two subpopulations, and adaptive competition is adopted between the subpopulations to enhance search efficiency. In addition, a restart mechanism is proposed in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{RefSet}$</tex-math> </inline-formula> update phase to ensure the diversity of solutions. The performance of the QCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the QCSS algorithm.

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.

Two-dimensional loading in vehicle routing problem with release and due dates

In this paper, we study a two-dimensional vehicle loading and routing problem in which customer orders with deadlines become available for dispatch as per their release dates. The objective is to minimize the sum of transportation, inventory, and tardiness costs while respecting various loading and routing constraints. This scenario allows us to study various tradeoffs that tend to arise due to temporal order aggregation across release dates. We thereby propose an integrated mathematical formulation to simultaneously model both the routing and loading requirements of the problem at hand. Specifically, as the problem is NP-hard, we propose a scatter search-based heuristic approach to solve large-size instances. Further, its performance is enhanced using problem-specific procedures and strategic oscillation approaches. Additionally, the numerical experiments illustrate the influence of cost structures on both the optimal loading configurations along with the optimal routes. Importantly, our experiments also suggest that the proposed scatter search method can produce good-quality solutions in less time.

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 knowledge-driven cooperative scatter search algorithm with reinforcement learning for the distributed blocking flow shop scheduling problem

The distributed flow shop scheduling problem has become one of the key problems related to the high efficiency impacted factor in the manufacturing industry due to its typical scenarios in real-world industrial applications. In this paper, a knowledge-driven cooperative scatter search (KCSS) is proposed to address the distributed blocking flow shop scheduling problem (DBFSP) to minimize the makespan. The scatter search (SS) is adopted as the basic optimization framework in KCSS. The neighborhood perturbation operator and the Q-learning algorithm are combined to select the appropriate perturbation operator in the search process. Firstly, considering the complexity of distributed scenarios, five search operators are used to construct a disturbance strategy pool. Secondly, the Q-learning algorithm dynamically chooses disturbance strategies to enhance exploration ability and search efficiency. Afterward, a local search method based on neighborhood reconstruction is proposed to perturb the currently found optimal solution to strengthen the ability of KCSS to develop in local areas. In addition, the path relinking mechanism is introduced into the subset combination method to guarantee the diversity of solutions in the optimization process. Finally, the performance of the KCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the KCSS algorithm. In addition, 518 of the best-known solutions out of 720 benchmark instances are updated.

Automatic Timetable Generation

Abstract: Generating a timetable manually for educational institutions can be a tedious task for educators, as each grade has a predefined education scheme and faculty workload that needs to be taken into account. The challenge lies in preparing a timetable that does not overlap with the schedules of the faculty members and can efficiently utilize all available resources. To overcome these difficulties, our project proposes the use of algorithms such as Evolutionary Algorithm, Tabu Search, Simulated Annealing, and scatter search. The proposed system will take inputs such as grade-wise subjects, teachers, and workload, and generate a possible timetable for the working days of the week. The system will integrate these inputs to make optimal use of all resources while adhering to the predefined constraints. This will help overcome the constraints that appear in the manual timetable generation process, resulting in timetables for any number of courses and grades. The implementation of this proposed system will provide a dynamic solution with the best approach, making it easier for educationalists to manage and set timetables. It will eliminate the complexity of manually generating and managing timetables, providing an efficient and effective solution to this challenging task