Mathematical modeling and a hybridized bacterial foraging optimization algorithm for the flexible job-shop scheduling problem with sequencing flexibility

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem (JSP) in which operations can be performed by a set of candidate capable machines. An extended version of the FJSP, entitled sequencing flexibility, is studied in this work, which considers precedence between the operations in the form of a directed acyclic graph instead of a sequential order. In this work, a mixed integer linear programming (MILP) formulation is presented to minimize weighted tardiness for the FJSP with sequencing flexibility. Due to the NP-hardness of the problem, a novel biomimicry hybrid bacterial foraging optimization algorithm (HBFOA) is developed, which is inspired by the behavior of E. coli bacteria in its search for food. The developed HBFOA search method is hybridized with simulated annealing (SA). Additionally, the algorithm has been enhanced by a local search method based on the manipulation of critical operations. Classical dispatching rules have been employed to create the initial swarm of HBFOA, and a new dispatching rule named minimum number of operations has been devised. The developed approach has been packaged in the form of a decision support system (DSS) developed on top of Microsoft Excel—a tool most small and mid-range enterprises (SME) use heavily for planning. A case study with local industry is presented to validate the proposed HBFOA and MILP. Additional numerical experiments using literature benchmarks are further used for validation. The results demonstrate that the HBFOA outperformed the classical dispatching rules and the best integer solution of MILP when minimizing the weighted tardiness and offered comparable results for the makespan instances.     

An Enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes

This paper addresses a sequence- and machine-dependent batch scheduling problem on a set of unrelated-parallel machines where the objective is to minimize a linear combination of total weighted completion time and total weighted tardiness. In particular, batch scheduling disregards the group technology assumptions by allowing for the possibility of splitting pre-determined groups of jobs into batches with respect to desired lower bounds on batch sizes. With regard to bounds on batch sizes, the MILP model is developed as two integrated batching and scheduling phases to present the problem. A benchmark of small-size instances on group scheduling shows the superior performance of batch scheduling up to 37% reduction in the objective function value. An efficient meta-heuristic algorithm based on tabu search with multi-level diversification and multi-tabu structure is developed at three levels, which moves back and forth between batching and scheduling phases. To eliminate searching in ineffective neighborhoods and thus enhance computational efficiency of search algorithms, several lemmas are proposed and proven. The results of applying lemmas reflect up to 40% reduction in computational times. Comparing the optimal solutions found by CPLEX and tabu search shows that the tabu search algorithm could find solutions, at least as good as CPLEX but in incredibly shorter computational time. In order to trigger the search algorithm, two different initial solution finding mechanisms have been developed and implemented. Also, due to lack of a qualified benchmark for unrelated-parallel machines, a comprehensive data generation mechanism has been developed in a way that it fairly reflects the real world situations encountered in practice. The machine availability times and job release times are considered to be dynamic and the run time of each job differs on different machines based upon the capability of the machines.     

A parallel hybrid local search algorithm for the container loading problem

In this contribution, a parallel hybrid local search algorithm for the three‐dimensional container loading problem (CLP) is proposed. First a simulated annealing method for the CLP is developed, which is then combined with an existing tabu search algorithm to form a hybrid metaheuristic. Finally, parallel versions are introduced for these algorithms. The emphasis is on CLP instances with a weakly heterogeneous load. Numerical tests based on the well‐known 700 test instances from Bischoff and Ratcliff are performed, and the outcome is compared with methods from other authors. The results show a high solution quality obtained with reasonable computing time.     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

A tabu search based hybrid evolutionary algorithm for the max-cut problem

This paper presents a tabu search based hybrid evolutionary algorithm (TSHEA) for solving the max-cut problem. The proposed algorithm integrates a distance-and-quality based solution combination operator and a tabu search procedure based on neighborhood combination of one-flip and constrained exchange moves. Comparisons with leading reference algorithms from the literature disclose that the proposed algorithm discovers new best solutions for 15 out of 91 instances, while matching the best known solutions on all but 4 instances. Analysis indicates that the neighborhood combination and the solution combination operator play key roles to the effectiveness of the proposed algorithm.     

Scheduling unrelated parallel machines with sequence-dependent setups

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms based on tabu search are developed to identify the best schedule that gives the minimum weighted tardiness. To enhance both the efficiency and efficacy of the search algorithms, four different initial solution finding mechanisms, based on dispatching rules, are developed. While there is no evidence of identifying solutions of better quality by employing a specific initial solution finding mechanism, the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both. Based on the extensive statistical analysis performed, the search algorithm with short-term memory and fixed tabu list size is recommended for solving small size problems, while that with long-term memory and minimum frequency for solving medium and large size problems, combined with fixed tabu list size for the former and variable tabu list size for the latter.     

Multi-objective optimization of the maritime cargo routing and scheduling problem

This paper addresses the multi-objective maritime cargo routing and scheduling problem, in which the delivery of bulk products from pickup to delivery ports is served by a heterogeneous fleet of vessels. A mixed integer linear programming (MILP) model is formulated to simultaneously minimize total operation costs, the scheduling makespan, and delays in selected deliveries. The model accounts for several real features, such as time windows, capacity of the vessel's compartments, and ports requirements. A fuzzy weighted max–min method was applied to solve the problem. Two heuristics were developed to effectively handle the complex generated MILP models during the solution process. Experiments were conducted to evaluate the optimization approach using real-life instances provided by a fertilizer company. Finally, a case study shows that the developed model and algorithmic framework are flexible and effective in coping with real problems, incorporating specific business rules from different companies.     

带作业范围约束的岸桥调度模型及其算法设计

受电缆线坑位置与缆线长度的限制,岸桥作业只能在一定的横向移动范围之内。考虑到这一现实要求,结合岸桥作业禁止跨越与安全距离等特有约束,以最小化装卸作业的makespan为目标,构建了新的岸桥作业调度混合整数规划模型。针对问题的NP-hard特性,设计了一种混合模拟退火算法,运用启发式算法生成质量较高的初始解,结合遗传算法的变异运算生成邻域新解,增强了解的多样性,引入禁忌搜索算法的禁忌表操作,避免了循环搜索,提高了求解效率。大规模实验结果表明所建立的模型是有效的,算法的求解质量与效率明显优于标准模拟退火算法与禁忌搜索算法。当实验规模逐渐增大时,与LINGO软件相比,算法在求解效率方面的优势越来越明显。     

Solving a leader–follower facility problem via parallel evolutionary approaches

A leader–follower facility problem is considered in this paper. The objective is to maximize the profit obtained by a chain (the leader) knowing that a competitor (the follower) will react by locating another single facility after the leader locates its own facility. A subpopulation-based evolutionary algorithm called TLUEGO was recently proposed to cope with this hard-to-solve global optimization problem. However, it requires high computational effort, even to manage small-size problems. In this work, three parallelizations of TLUEGO are proposed, a distributed memory programming algorithm, a shared memory programming algorithm, and a hybrid of the two previous algorithms, which not only allow us to obtain the solution faster, but also to solve larger instances.     

Solution method for the location planning problem of logistics park with variable capacity

In this paper we study a logistics park location planning problem in which the capacity of the logistics park is determined by the sectors used to establish it in an open site. Since the size of each sector is not necessarily the same in every potential site, the capacity of the logistics park is thus variable, which makes this problem different from the traditional location problems in which the capacity of each facility is fixed. The task of this problem is to determine the location of the logistics parks, the sectors to be used to establish the logistics park in each open site, and the allocation of customers to the established logistics parks so as to minimize the total costs for establishing the logistics parks and supplying the demands of customers. The size mode is introduced to deal with the nonlinear establishment cost function and consequently this problem is formulated as an integer linear programming (ILP) model. Since CPLEX can only solve the ILP model with small-size problems, a tabu search (TS) hybrid with filter and fan (F&F) is presented to obtain near optimal solutions. In the hybrid algorithm, the TS is used to improve the solution by changing the allocation of customers to open sites while the F&F is used to further improve the solution by adjusting the status of sites (i.e., open or closed). In addition, an elite solution pool is constructed to store good solutions found in the searching history. Whenever the hybrid algorithm is trapped in local minima, a new start solution will be generated from the elite pool so as to improve the search diversity. To evaluate the performance of the proposed hybrid TS method, the column generation (CG) method with an acceleration strategy is developed to provide tight lower bounds. Computational results showed that the proposed hybrid algorithm can obtain optimal solutions for most of the small size problems and satisfactory near-optimal solutions with comparison to lower bounds for large size problems.     

Improvements of constraint programming and hybrid methods for scheduling of tests on vehicle prototypes

In the automotive industry, a manufacturer must perform several hundreds of tests on prototypes of a vehicle before starting its mass production. Tests must be allocated to suitable prototypes and ordered to satisfy temporal constraints and various kinds of test dependencies. The manufacturer aims to minimize the number of prototypes required. We present improvements of constraint programming (CP) and hybrid approaches to effectively solve random instances from an existing benchmark. CP mostly achieves better solutions than the previous heuristic technique and genetic algorithm. We also provide customized search schemes to enhance the performance of general search algorithms. The hybrid approach applies mixed integer linear programming (MILP) to solve the planning part and CP to find the complete schedule. We consider several logical principles such that the MILP model can accurately estimate the prototype demand, while its size particularly for large instances does not exceed memory capacity. Moreover, the robustness is alleviated when we allow CP to partially change the allocation obtained from the MILP model. The hybrid method can contribute to optimal solutions in some instances.     

Mathematical modeling and heuristic approaches to flexible job shop scheduling problems

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem in medium and actual size problem with traditional optimization approaches owing to the high computational complexity. For solving the realistic case with more than two jobs, two types of approaches have been used: hierarchical approaches and integrated approaches. In hierarchical approaches assignment of operations to machines and the sequencing of operations on the resources or machines are treated separately, i.e., assignment and sequencing are considered independently, where in integrated approaches, assignment and sequencing are not differentiated. In this paper, a mathematical model and heuristic approaches for flexible job shop scheduling problems (FJSP) are considered. Mathematical model is used to achieve optimal solution for small size problems. Since FJSP is NP-hard problem, two heuristics approaches involve of integrated and hierarchical approaches are developed to solve the real size problems. Six different hybrid searching structures depending on used searching approach and heuristics are presented in this paper. Numerical experiments are used to evaluate the performance of the developed algorithms. It is concluded that, the hierarchical algorithms have better performance than integrated algorithms and the algorithm which use tabu search and simulated annealing heuristics for assignment and sequencing problems consecutively is more suitable than the other algorithms. Also the numerical experiments validate the quality of the proposed algorithms.     

A scheduling problem in blocking hybrid flow shop robotic cells with multiple robots

This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part types, unrelated parallel machines, multiple robots and machine eligibility constraints. Initially, a mixed integer linear programming (MILP) model is proposed to minimize the makespan for this problem. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed for its solution. To increase the efficiency of the SA algorithm, a new neighborhood structure based on block properties is applied. The performance of the proposed SA is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighborhood structure. Additionally, this study shows that the appropriate number of robots depends on the sequence of processing operations to be performed at each stage.     

禁忌搜索与固定变量结合的启发式算法求解UBQP

提出了将固定变量与禁忌搜索结合的启发式算法来求解UBQP。此算法包含两个阶段：采用禁忌搜索得到一个参考解;根据该参考解固定或释放若干变量。选择固定变量还是释放变量由搜索的历史信息决定。此算法动态地在禁忌搜索与固定或释放变量这两个阶段之间交替进行,直到停机条件满足为止。用提出的算法对国际文献中公认的15个难算例进行实算测试,得到了全部测试算例的最优解。实验结果表明,该算法是求解UBQP的一个高效求解算法。     

A Memetic Approach to the Nurse Rostering Problem

Constructing timetables of work for personnel in healthcare institutions is known to be a highly constrained and difficult problem to solve. In this paper, we discuss a commercial system, together with the model it uses, for this rostering problem. We show that tabu search heuristics can be made effective, particularly for obtaining reasonably good solutions quickly for smaller rostering problems. We discuss the robustness issues, which arise in practice, for tabu search heuristics. This paper introduces a range of new memetic approaches for the problem, which use a steepest descent improvement heuristic within a genetic algorithm framework. We provide empirical evidence to demonstrate the best features of a memetic algorithm for the rostering problem, particularly the nature of an effective recombination operator, and show that these memetic approaches can handle initialisation parameters and a range of instances more robustly than tabu search algorithms, at the expense of longer solution times. Having presented tabu search and memetic approaches (both with benefits and drawbacks) we finally present an algorithm that is a hybrid of both approaches. This technique produces better solutions than either of the earlier approaches and it is relatively unaffected by initialisation and parameter changes, combining some of the best features of each approach to create a hybrid which is greater than the sum of its component algorithms.     

Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem

This paper presents a new hybrid algorithm that executes large neighbourhood search algorithm in combination with the solution construction mechanism of the ant colony optimization algorithm (LNS–ACO) for the capacitated vehicle routing problem (CVRP). The proposed hybrid LNS–ACO algorithm aims at enhancing the performance of the large neighbourhood search algorithm by providing a satisfactory level of diversification via the solution construction mechanism of the ant colony optimization algorithm. Therefore, LNS–ACO algorithm combines its solution improvement mechanism with a solution construction mechanism. The performance of the proposed algorithm is tested on a set of CVRP instances. The hybrid LNS–ACO algorithm is compared against two other LNS variants and some of the formerly developed methods in terms of solution quality. Computational results indicate that the proposed hybrid LNS–ACO algorithm has a satisfactory performance in solving CVRP instances.     

Variable Neighborhood Search heuristic for the Inventory Routing Problem in fuel delivery

In this paper we observe the extension of the vehicle routing problem (VRP) in fuel delivery that includes petrol stations inventory management and which can be classified as the Inventory Routing Problem (IRP) in fuel delivery. The objective of the IRP is to minimize the total cost of vehicle routing and inventory management. We developed a Variable Neighborhood Search (VNS) heuristic for solving a multi-product multi-period IRP in fuel delivery with multi-compartment homogeneous vehicles, and deterministic consumption that varies with each petrol station and each fuel type. The stochastic VNS heuristic is compared to a Mixed Integer Linear Programming (MILP) model and the deterministic “compartment transfer” (CT) heuristic. For three different scale problems, with different vehicle types, the developed VNS heuristic outperforms the deterministic CT heuristic. Also, for the smallest scale problem instances, the developed VNS was capable of obtaining the near optimal and optimal solutions (the MILP model was able to solve only the smallest scale problem instances).     

Hybrid genetic algorithmsfor a multiple-objective scheduling problem

This paper describes the characteristics of two hybrid genetic algorithms (GAs) for generating allocation and sequencing of production lots in a flow-shop environment based on a non-linear, multi-criteria objective function. Both GAs are used as search techniques: in the first model the task of the GA is to allocate and sequence the jobs; in the second model, the GA is combined with a dispatching rule (Earliest Due Date, EDD) thus limiting its task only on the allocation of the jobs. Both GAs are characterized by a dynamic population size with dynamic birth rate, as well as by multiple-operator reproduction criteria and by adaptive crossover and mutation rates. A discrete-event simulation model has been used in order to evaluate the performances of the tentative schedules. The proposed algorithms have been subsequently compared with a classical branch and bound method.     

A hybrid metaheuristic approach for the capacitated p-median problem

The capacitated p-median problem (CPMP) seeks to obtain the optimal location of p medians considering distances and capacities for the services to be given by each median. This paper presents an efficient hybrid metaheuristic algorithm by combining a proposed cutting-plane neighborhood structure and a tabu search metaheuristic for the CPMP. In the proposed neighborhood structure to move from the current solution to a neighbor solution, an open median is selected and closed. Then, a linear programming (LP) model is generated by relaxing binary constraints and adding new constraints. The generated LP solution is improved using cutting-plane inequalities. The solution of this strong LP is considered as a new neighbor solution. In order to select an open median to be closed, several strategies are proposed. The neighborhood structure is combined with a tabu search algorithm in the proposed approach. The parameters of the proposed hybrid algorithm are tuned using design of experiments approach. The proposed algorithm is tested on several sets of benchmark instances. The statistical analysis shows efficiency and effectiveness of the hybrid algorithm in comparison with the best approach found in the literature.     

A heuristic block coordinate descent approach for controlled tabular adjustment

One of the main concerns of national statistical agencies (NSAs) is to publish tabular data. NSAs have to guarantee that no private information from specific respondents can be disclosed from the released tables. The purpose of the statistical disclosure control field is to avoid such a leak of private information. Most protection techniques for tabular data rely on the formulation of a large mathematical programming problem, whose solution is computationally expensive even for tables of moderate size. One of the emerging techniques in this field is controlled tabular adjustment (CTA). Although CTA is more efficient than other protection methods, the resulting mixed integer linear problems (MILP) are still challenging. In this work a heuristic approach based on block coordinate descent decomposition is designed and applied to large hierarchical and general CTA instances. This approach is compared with CPLEX, a state-of-the-art MILP solver. Our results, from both synthetic and real tables with up to 1,200,000 cells, 100,000 of them being sensitive (resulting in MILP instances of up to 2,400,000 continuous variables, 100,000 binary variables, and 475,000 constraints) show that the heuristic block coordinate descent has a better practical behavior than a state-of-the-art solver: for large hierarchical instances it provides significantly better solutions within a specified realistic time limit, as required by NSAs in real-world.