An improved stepsize of the subgradient algorithm for solving the lagrangian relaxation problem

The Lagrangian relaxation approach has been successfully applied to many large-scale mathematical programming problems. The Lagrangian relaxation problem itself is a non-differentiable optimization problem. One of the methods for solving such problem is the subgradient algorithm. In this paper, we propose an improved stepsize of the subgradient algorithm for solving the Lagrangian relaxation problem. Our version of the algorithm may significantly improve the rate of convergence of subgradient algorithm when applied to the solution of Lagrangian relaxation problem. An illustrative numerical example is also given.     

Variable neighbourhood search for the variable sized bin packing problem

The variable sized bin packing problem is a generalisation of the one-dimensional bin packing problem. Given is a set of weighted items, which must be packed into a minimum-cost set of bins of variable sizes and costs. This problem has practical applications, for example, in packing, transportation planning, and cutting. In this work we propose a variable neighbourhood search metaheuristic for tackling the variable sized bin packing problem. The presented algorithm can be seen as a hybrid metaheuristic, because it makes use of lower bounding techniques and dynamic programming in various algorithmic components. An extensive experimentation on a diverse set of problem instances shows that the proposed algorithm is very competitive with current state-of-the-art approaches.     

冷链物流越库调度的拉格朗日松弛算法

为了提高冷链物流的运输效率,解决越库在冷链物流中的应用问题,提出了基于拉格朗日松弛算法的冷链物流的越库调度方法.首先进行了问题域的描述并做出了具体假设,基于问题域以最小化卡车等待时间和越库内部运输成本为目标,建立越库调度的整数规划数学模型.然后,提出了针对越库调度模型的拉格朗日松弛算法,松弛复杂约束后根据决策变量将松弛...     

Minimizing makespan in permutation flow shop scheduling problems using a hybrid metaheuristic algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in permutation flow shop scheduling problems. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on a greedy randomized constructive heuristic, a genetic algorithm (GA) for solution evolution, and a variable neighbourhood search (VNS) to improve the population. The hybridization of a GA with VNS, combining the advantages of these two individual components, is the key innovative aspect of the approach. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches high-quality solutions in short computational times. Furthermore, it requires very few user-defined parameters, rendering it applicable to real-life flow shop scheduling problems.     

Variable Neighborhood Search for extremal vertices : The AutoGraphiX-III system

More than fifteen years after the beginning of the development of AutoGraphiX (AGX), a third version of the software is made available. Since the program was rewritten from scratch, it was the opportunity to look forward and consider new avenues. From the user׳s point of view, the interface is completely changed, which allows the display of multiple information which was not possible in the previous versions. However, one of the main improvements is that it is designed to help researchers in the field of complex networks. In these days when increasing research is applied to complex networks (such as social networks), the use of quantities related to vertices, indicating the centrality (the importance of an actor in the network measured as a topological indicator) naturally leads researchers toward the mathematical study of these quantities. This new paradigm implies a complete change in the optimization algorithm that now natively handles multi objective optimization problems involving vertex-related measures.     

Fuzzy J-Means: a new heuristic for fuzzy clustering

A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called Fuzzy J-Means, where the neighbourhood is defined by all possible centroid-to-pattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the well-known Fuzzy C-Means heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.     

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems.     

A bilevel decomposition algorithm for simultaneous production scheduling and conflict-free routing for automated guided vehicles

We address a bilevel decomposition algorithm for solving the simultaneous scheduling and conflict-free routing problems for automated guided vehicles. The overall objective is to minimize the total weighted tardiness of the set of jobs related to these tasks. A mixed integer formulation is decomposed into two levels: the upper level master problem of task assignment and scheduling; and the lower level routing subproblem. The master problem is solved by using Lagrangian relaxation and a lower bound is obtained. Either the solution turns out to be feasible for the lower level or a feasible solution for the problem is constructed, and an upper bound is obtained. If the convergence is not satisfied, cuts are generated to exclude previous feasible solutions before solving the master problem again. Two types of cuts are proposed to reduce the duality gap. The effectiveness of the proposed method is investigated from computational experiments.     

A variable neighborhood search for the multi-depot vehicle routing problem with loading cost

The purpose of this paper is to propose a variable neighbourhood search (VNS) for solving the multi-depot vehicle routing problem with loading cost (MDVRPLC). The MDVRPLC is the combination of multi-depot vehicle routing problem (MDVRP) and vehicle routing problem with loading cost (VRPLC) which are both variations of the vehicle routing problem (VRP) and occur only rarely in the literature. In fact, an extensive literature search failed to find any literature related specifically to the MDVRPLC. The proposed VNS comprises three phases. First, a stochastic method is used for initial solution generation. Second, four operators are randomly selected to search neighbourhood solutions. Third, a criterion similar to simulated annealing (SA) is used for neighbourhood solution acceptance. The proposed VNS has been test on 23 MDVRP benchmark problems. The experimental results show that the proposed method provides an average 23.77% improvement in total transportation cost over the best known results based on minimizing transportation distance. The results show that the proposed method is efficient and effective in solving problems.     

A revised electromagnetism-like mechanism for layout design of reconfigurable manufacturing system

The layout design problem is one of the most important issues for manufacturing system design and control. A revised electromagnetism-like mechanism (REM) is proposed in this paper for the layout design of reconfigurable manufacturing systems utilizing automated guided vehicle. First, the formal model considering both loaded and empty flows is given. Then the REM is developed to solve the proposed model. In the REM, particles are encoded discretely. The charge of a particle is calculated according the total material handling cost of the particle. In the local search procedure, variable neighbourhood search strategy based on Hamming distance is adopted. In the moving procedure, the particles are moved according to the ordering of each element. To verify the effect of the proposed method, several computation cases are carried out. The computation results show that the proposed method is able to get optimal solutions for small scale problems and near optimal solutions within limited computation time for large scale problems. This indicates that the proposed method is effective and efficient.     

A memetic algorithm for the flexible flow line scheduling problem with processor blocking

This paper introduces an efficient memetic algorithm (MA) combined with a novel local search engine, namely, nested variable neighbourhood search (NVNS), to solve the flexible flow line scheduling problem with processor blocking (FFLB) and without intermediate buffers. A flexible flow line consists of several processing stages in series, with or without intermediate buffers, with each stage having one or more identical parallel processors. The line produces a number of different products, and each product must be processed by at most one processor in each stage. To obtain an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches and optimization tools is extremely difficult. Our proposed MA employs a new representation, operators, and local search method to solve the above-mentioned problem. The computational results obtained in experiments demonstrate the efficiency of the proposed MA, which is significantly superior to the classical genetic algorithm (CGA) under the same conditions when the population size is increased in the CGA.     

A multi-phase oscillated variable neighbourhood search algorithm for a real-world open vehicle routing problem

The aim of this study is to solve the newspaper delivery optimization problem for a media delivery company in Turkey by reducing the total cost of carriers. The problem is modelled as an open vehicle routing problem (OVRP), which is a variant of the vehicle routing problem. A variable neighbourhood search-based algorithm is proposed to solve a real-world OVRP. The proposed algorithm is tested with varieties of small and large-scale benchmark suites and a very large-scale real-world problem instance. The results of the proposed algorithm provide either the best known solution or a competitive solution for each of the benchmark instances. The algorithm also improves the real-world company’s solutions by more than 10%.     

Variable neighborhood descent with iterated local search for routing and wavelength assignment

In this work we treat the Routing and Wavelength Assignment (RWA) with focus on minimizing the number of wavelengths to route demand requests. Lightpaths are used to carry the traffic optically between origin-destination pairs. The RWA is subjected to wavelength continuity constraints, and a particular wavelength cannot be assigned to two different lightpaths sharing a common physical link. We develop a Variable Neighborhood Descent (VND) with Iterated Local Search (ILS) for the problem. In a VND phase we try to rearrange requests between subgraphs associated to subsets of a partition of the set of lightpath requests. In a feasible solution, lightpaths belonging to a subset can be routed with the same wavelength. Thus, the purpose is to eliminate one subset of the partition. When VND fails, we perform a ILS phase to disturb the requests distribution among the subsets of the partition. An iteration of the algorithm alternates between a VND phase and a ILS phase. We report computational experiments that show VND-ILS was able to improve results upon powerful methods proposed in the literature.