Engineering an efficient two‐phase local search algorithm for the co‐rotating twin‐screw extruder configuration problem

The twin‐screw configuration problem arises during polymer extrusion and compounding. It consists in defining the location of a set of pre‐defined screw elements along the screw axis in order to optimize different, typically conflicting objectives. In this paper, we present a simple yet effective stochastic local search (SLS) algorithm for this problem. Our algorithm is based on efficient single‐objective iterative improvement algorithms, which have been developed by studying different neighborhood structures, neighborhood search strategies, and neighborhood restrictions. These algorithms are embedded into a variation of the two‐phase local search framework to tackle various bi‐objective versions of this problem. An experimental comparison with a previously proposed multi‐objective evolutionary algorithm shows that a main advantage of our SLS algorithm is that it converges faster to a high‐quality approximation to the Pareto front.     

An efficient memetic algorithm for solving the job shop scheduling problem

The job shop scheduling problem (JSP) is well known as one of the most complicated combinatorial optimization problems, and it is a NP-hard problem. Memetic algorithm (MA) which combines the global search and local search is a hybrid evolutionary algorithm. In this paper, an efficient MA with a novel local search is proposed to solve the JSP. Within the local search, a systematic change of the neighborhood is carried out to avoid trapping into local optimal. And two neighborhood structures are designed by exchanging and inserting based on the critical path. The objective of minimizing makespan is considered while satisfying a number of hard constraints. The computational results obtained in experiments demonstrate that the efficiency of the proposed MA is significantly superior to the other reported approaches in the literature.     

Tabu search with multi-level neighborhood structures for high dimensional problems

Metaheuristics have been successfully applied to solve different types of numerical and combinatorial optimization problems. However, they often lose their effectiveness and advantages when applied to large and complex problems. Moreover, the contributions of metaheuristics that deal with high dimensional problems are still very limited compared with low and middle dimensional problems. In this paper, Tabu Search algorithm based on variable partitioning is proposed for solving high dimensional problems. Specifically, multi-level neighborhood structures are constructed by partitioning the variables into small groups. Some of these groups are selected and the neighborhood of their variables are explored. The computational results shown later indicate that exploring the neighborhood of all variables at the same time, even for structured neighborhood, can badly effect the progress of the search. However, exploring the neighborhood gradually through smaller number of variables can give better results. The variable partitioning mechanism used in the proposed method can allow the search process to explore the region around the current iterate solution more precisely. Actually, this partitioning mechanism works as dimensional reduction mechanism. For high dimensional problems, extensive computational studies are carried out to evaluate the performance of newly proposed algorithm on large number of benchmark functions. The results show that the proposed method is promising and produces high quality solutions within low computational costs.     

A variable neighborhood search heuristic algorithm for the double vehicle routing problem with multiple stacks

This paper addresses the double vehicle routing problem with multiple stacks (DVRPMS) in which a fleet of vehicles must collect items in a pickup region and then travel to a delivery region where all items are delivered. The load compartment of all vehicles is divided into rows (horizontal stacks) of fixed profundity (horizontal heights), and on each row, the unloading process must respect the last‐in‐first‐out policy. The objective of the DVRPMS is to find optimal routes visiting all pickup and delivery points while ensuring the feasibility of the vehicle loading plans. We propose a new integer linear programming formulation, which was useful to find inconsistencies in the results of exact algorithms proposed in the literature, and a variable neighborhood search based algorithm that was able to find solutions with same or higher quality in shorter computational time for most instances when compared to the methods already present in the literature.     

Modeling and solving assembly line design problems by considering human factors with a real‐life application

Ergonomics has been playing an important role in assembly system design (ASD) that contains not only the main assembly line balancing problem but also the subassembly line balancing and assembly layout problem. The ergonomics in ASD has an impact both on productivity and on workers’ health, especially when frequent changes in the product mix occur. In this study, we propose a systematic approach in order to handle ASD, which consists of three subproblems, while considering ergonomic risk factors. The first two subproblems are solved simultaneously using the proposed rule‐based constructive search algorithm, where ergonomic risks are evaluated by OCRA method. Later, layout problem is solved under transportation constraints using local search methods with various neighborhood structures. To provide the applicability and evaluate the performance of the proposed systematic approach, a real‐life case study in a harness manufacturing company is solved and prototype productions are performed.     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.     

A branch-and-cut approach for the vehicle routing problem with loading constraints

In this paper we describe a branch-and-cut algorithm for the vehicle routing problem with unloading constraints. The problem is to determine a set of routes with minimum total cost, each route leaving a depot, such that all clients are visited exactly once. Each client has a demand, given by a set of items, that are initially stored in a depot. We consider the versions of the problem with two and tri dimensional parallelepiped items. For each route in a solution, we also need to construct a feasible packing for all the items of the clients in this route. As it would be too expensive to rearrange the vehicle cargo when removing the items of a client, it is important to perform this task without moving the other client items. Such packings are said to satisfy unloading constraints.In this paper we describe a branch-and-cut algorithm that uses several techniques to prune the branch-and-cut enumeration tree. The presented algorithm uses several packing routines with different algorithmic approaches, such as branch-and-bound, constraint programming and metaheuristics. The careful combination of these routines showed that the presented algorithm is competitive, and could obtain optimum solutions within significantly smaller computational times for most of the instances presented in the literature.     

A study on integrating sequence dependent setup time flexible flow lines and preventive maintenance scheduling

This paper investigates flexible flow line problems with sequence dependent setup times and different preventive maintenance policies. The optimization criterion is the minimization of makespan. The contribution of this work could be divided into two parts: (1) Since the proposed integrating methods in the literature are often not only complicated but also problem-specific, we have been thinking of providing a technique simple to implement, yet easily extendible to any other machine scheduling problems to overcome the foregoing drawbacks. (2) In order to tackle the problem, we propose a novel variable neighborhood search (VNS) as well as the adaptations of some existing high performing metaheuristics in the literature. The proposed VNS uses advanced neighborhood search structures. In order to evaluate the algorithms, a benchmark is established with the meticulous care. All the results illustrate that the VNS outperforms the other algorithms.     

Artificial intelligence search methods for multi-machine two-stage scheduling with due date penalty,inventory, and machining costs

This paper evaluates artificial intelligence search methods for multi-machine two-stage scheduling problems with due date penalty, inventory, and machining costs. We compare four search methods: tabu search, simulated annealing, genetic algorithm, and neighborhood search. Computational results show that the tabu search performs best in terms of solution quality. The tabu search also requires much less computational time than the genetic algorithm and simulated annealing. As expected, the neighborhood search needs the smallest computational time, but gives the worst solution quality. To further improve the solution quality and computational time, this paper proposes a two-phase tabu search. The two-phase tabu search sequentially addresses two aspects of sequencing for the same problem, order- and component-based sequencing. The order-based tabu search identifies a sequence for customers’ orders. Starting from the sequence identified for customers’ orders, the component-based tabu search fine-tunes the sequence for components produced at the fabrication stage. The results show that the two-phase tabu search is better in solution quality and computational time than the one-phase tabu search. The difference in solution quality is more pronounced at the early stage of the search.Scope and purposeMost manufacturing firms have some form of separate fabrication and assembly stages. Raw materials are transformed into components at the fabrication stage and the components are then assembled into finished products at the assembly stage. The components and assembly items are typically routed in batch quantities through several machines/work centers in a predetermined order before the finished products are delivered to customers.In this study, we model fabrication and assembly work centers as multi-machine two-stage manufacturing systems where a given machine is used to assemble/produce at least one component/product. The scheduling problem considered in this study involves a scheduling decision that achieves three objectives concurrently: (1) meeting customers’ due dates, (2) minimizing inventory cost, and (3) minimizing machining cost. Each order is an indivisible scheduling element that needs to be delivered to customers on the due date. Each order triggers successive production events from upstream to downstream according to the bill-of-material structure between components and end products.The objective of this paper are three-fold: (1) to present a solution representation for the multi-machine two-stage scheduling problem, (2) to identify the best artificial intelligence search method for this problem based on extensive computational experiments, and (3) to propose a modified tabu search method to further improve the solution quality and computational time.     

Ejection chain moves for automatic neighborhood synthesis in constrained cardinality‐minimization problems

In this paper, we deal with the problem of automatically synthesizing “good” neighborhoods for a specific class of problems, namely constrained cardinality‐minimization problems. Exploiting the peculiarity of the objective function of such problems, we develop automatic ejection chain moves that define neighborhood structures to be explored with a black‐box solver. In particular, starting from a formulation of a cardinality‐minimization problem and a feasible solution, our procedure automatically detects the “entities” involved in the problem and learns the strength of the relationships among them. This information is then used to define the characteristics of our moves that consist in ejecting one entity at a time from the solution. If one of such moves results in an infeasible solution, then feasibility is recovered by performing an additional step based on the solution of an auxiliary problem. The computational results show that, when assessed on four well‐known constrained cardinality‐minimization problems, our approach outperforms both a black‐box mixed integer programming solver and a state‐of‐the‐art model‐based neighborhood search procedure with respect to both solution quality and computing times.     

Use of biased neighborhood structures in multiobjective memetic algorithms

In this paper, we examine the use of biased neighborhood structures for local search in multiobjective memetic algorithms. Under a biased neighborhood structure, each neighbor of the current solution has a different probability to be sampled in local search. In standard local search, all neighbors of the current solution usually have the same probability because they are randomly sampled. On the other hand, we assign larger probabilities to more promising neighbors in order to improve the search ability of multiobjective memetic algorithms. In this paper, we first explain our multiobjective memetic algorithm, which is a simple hybrid algorithm of NSGA-II and local search. Then we explain its variants with biased neighborhood structures for multiobjective 0/1 knapsack and flowshop scheduling problems. Finally we examine the performance of each variant through computational experiments. Experimental results show that the use of biased neighborhood structures clearly improves the performance of our multiobjective memetic algorithm.     

Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

In this paper, we address the constrained two‐dimensional rectangular guillotine single large placement problem (2D_R_CG_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D_R_CG_SLOPP, which consider only two‐staged or one‐group patterns. Finally, as a specific solution method for the 2D_R_CG_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch‐and‐Benders‐cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions.     

A comparison of five heuristics for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times.     

双邻域查找组播聚合算法

光传输网络中聚合组播问题是一个完全NP 难问题,提出了一种解决聚合组播问题的双邻域查找算法.该算法使得生成的聚合树数量在满足波长约束的前提下,带宽浪费比率尽可能地小.基于贪婪策略定义了一种优先聚合规则以生成初始解;定义了两种邻域结构,使邻域查找具有效率;提出了跳坑策略以跳出局部最优解并且将查找引向有希望的方向.模拟实验结果表明:该算法可以有效地进行组播树的聚合,当轻载时,组播组阻塞比率始终为0;当重载时,与其他算法相比,平均带宽浪费比率降低25%以上.因此,对不同的网络状况都能获得较好的性能.     

Scheduling jobs with ready times and precedence constraints on parallel batch machines using metaheuristics

In this paper, we discuss a scheduling problem for parallel batch machines where the jobs have ready times. Problems of this type can be found in semiconductor wafer fabrication facilities (wafer fabs). In addition, we consider precedence constraints among the jobs. Such constraints arise, for example, in scheduling subproblems of the shifting bottleneck heuristic when complex job shop scheduling problems are tackled. We use the total weighted tardiness as the performance measure to be optimized. Hence, the problem is NP-hard and we have to rely on heuristic solution approaches. We consider a variable neighborhood search (VNS) scheme and a greedy randomized adaptive search procedure (GRASP) to compute efficient solutions. We assess the performance of the two metaheuristics based on a large set of randomly generated problem instances and based on instances from the literature. The obtained computational results demonstrate that VNS is a very fast heuristic that quickly leads to high-quality solutions, whereas the GRASP is slightly outperformed by the VNS approach. However, the GRASP approach has the advantage that it can be parallelized in a more natural manner compared to VNS.     

Extended guided tabu search and a new packing algorithm for the two-dimensional loading vehicle routing problem

In this paper, we develop an extended guided tabu search (EGTS) and a new heuristic packing algorithm for the two-dimensional loading vehicle routing problem (2L-CVRP). The 2L-CVRP is a combination of two well-known NP-hard problems, the capacitated vehicle routing problem, and the two-dimensional bin packing problem. It is very difficult to get a good performance solution in practice for these problems. We propose a meta-heuristic methodology EGTS which incorporates theories of tabu search and extended guided local search (EGLS). It has been proved that tabu search is a very good approach for the CVRP, and the guiding mechanism of the EGLS can help tabu search to escape effectively from local optimum. Furthermore, we have modified a collection of packing heuristics by adding a new packing heuristic to solve the loading constraints in 2L-CVRP, in order to improve the cost function significantly. The effectiveness of the proposed algorithm is tested, and proven by extensive computational experiments on benchmark instances.     

An integration of mixed VND and VNS: the case of the multivehicle covering tour problem

The multivehicle covering tour problem (m‐CTP) is a transportation problem with different kinds of locations, where a set of locations must be visited while another set must be close enough to planned routes. Given two sets of vertices V and W, where V represents the set of vertices that may be visited and W is a set of vertices that must be covered by up to m vehicles, the m‐CTP problem is to minimize vehicle routes on a subset of V including T, which represents the subset of vertices that must be visited through the use of potential locations in V. The variant of m‐CTP without a route‐length constraint is treated in this paper. To tackle this problem, we propose a variable neighborhood search heuristic based on variable neighborhood descent method. Experiments were conducted using the datasets based on traveling salesman problem library instances.     

Multi-objective scheduling and a resource allocation problem in hospitals

This study addresses the issue of scheduling medical treatments for resident patients in a hospital. Schedules are made daily according to the restrictions on medical equipment and physicians who are being assigned at the same time. The problem is formulated as a multi-objective binary integer programming (BIP) model. Three types of metaheuristics are proposed and implemented to deal with the discrete search space, numerous variables, constraints and multiple objectives: a variable neighborhood search (VNS)-based method, scatter search (SS)-based methods and a non-dominated sorting genetic algorithm (NSGA-II). This paper also provides the results of computational experiments and compares their ability to find efficient solutions to the multi-objective scheduling problem.     

Variable neighborhood search for location routing

In this paper we propose various neighborhood search heuristics (VNS) for solving the location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. The objective is to find depot locations and to design least cost routes for vehicles. We integrate a variable neighborhood descent as the local search in the general variable neighborhood heuristic framework to solve this problem. We propose five neighborhood structures which are either of routing or location type and use them in both shaking and local search steps. The proposed three VNS methods are tested on benchmark instances and successfully compared with other two state-of-the-art heuristics.