An efficient implementation of a VNS/ILS heuristic for a real-life car sequencing problem

The car sequencing problem consists in sequencing a given set of cars to be produced in a single day. We address one of the variants of this problem, in which the objective of minimizing the number of violations of assembly constraints has a stronger weight than the minimization of the number of paint color changes. We present and describe in details a VNS/ILS approach for approximately solving this problem. Computational results on real-life test instances are reported. The work presented in this paper obtained the second prize in the challenge ROADEF’2005 sponsored by Renault.     

A hybrid heuristic for a multi-objective real-life car sequencing problem with painting and assembly line constraints

We address a multi-objective version of the car sequencing problem, which consists in sequencing a given set of cars to be produced in a single day, minimizing the number of violations of assembly constraints and the number of paint color changes in the production line. We propose a set of heuristics for approximately solving this problem, based on the paradigms of the VNS and ILS metaheuristics, to which further intensification and diversification strategies have been added. Computational results on real-life test instances are reported. The work presented in this paper obtained the second prize in the ROADEF challenge 2005 sponsored by Renault.     

On the complexity of the car sequencing problem

In this note we give an easier proof of the known result that the car sequencing problem is NP-hard, and point out that it is NP-hard in the strong sense. We show that a previous claim of NP-completeness is incorrect, and instead we give a sufficient condition of membership of NP. We also provide a pseudo-polynomial algorithm for a special case.     

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.     

The impact of energy function structure on solving generalized assignment problem using Hopfield neural network

In the last 20 years, neural networks researchers have exploited different penalty based energy functions structures for solving combinatorial optimization problems (COPs) and have established solutions that are stable and convergent. These solutions, however, have in general suffered from lack of feasibility and integrality. On the other hand, operational researchers have exploited different methods for converting a constrained optimization problem into an unconstrained optimization problem. In this paper we have investigated these methods for solving generalized assignment problems (GAPs). Our results concretely establishes that the augmented Lagrangean method can produce superior results with respect to feasibility and integrality, which are currently the main concerns in solving neural based COPs.     

Two local search approaches for solving real-life car sequencing problems

The NP-hard problem of car sequencing appears as the heart of the logistic process of many car manufacturers. The subject of the ROADEF’2005 challenge addressed a car sequencing problem proposed by the car manufacturer RENAULT, more complex than the academic problem generally addressed in the literature. This paper describes two local search approaches for this problem. In the first part, a new approach by very large-scale neighborhood search is presented. This approach, designed during the qualification stage preceding the final, is based on an original integer linear programming formulation. The second part is dedicated to the approach which enabled us to win the ROADEF’2005 challenge. Inspired by the latest works on the subject, this one is based on very fast explorations of small neighborhoods. Our contribution here is mainly algorithmic, in particular by showing how much exploiting invariants speeds up the neighborhood evaluation and contributes to the diversification of the search. Finally, the two approaches are compared and discussed through an extensive computational study on RENAULT’s benchmarks. The main conclusion drawn at this point is that sophisticated metaheuristics are useless to solve car sequencing problems. More generally, our victory on ROADEF’2005 challenge demonstrates that algorithmic aspects, sometimes neglected, remain the key ingredients for designing and engineering high-performance local search heuristics.     

An efficient heuristic approach for a multi-period logistics network redesign problem

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks.     

Solving the car sequencing problem via Branch & Bound

In a mixed-model assembly line, varying models of the same basic product are to be produced in a facultative sequence. This results to a short-term planning problem where a sequence of models is sought which minimizes station overloads. In practice – e.g. the final assembly of cars – special sequencing rules are enforced which restrict the number of models possessing a certain optional feature k to r_k within a subsequence of s_k successive models. This problem is known as car sequencing. So far, employed solution techniques stem mainly from the field of Logic and Constraint Logic Programming. In this work, a special Branch & Bound algorithm is developed, which exploits the problem structure in order to reduce combinatorial complexity.     

Dynamical behaviors of Hopfield neural network with multilevel activation functions

When the activation function possesses multilevel property, the Hopfield neural network has some novel dynamical behaviors, and it is worthwhile to study. First, some properties about the activation function are obtained, on this foundation, some theoretical analysis about the quasi-equilibrium points has been made. From local and global view, some theorems about the boundedness are presented. Finally, two theorems about the first derivative of trajectory with respect to time are found, the first theorem indicates that the trajectory cannot keep increasing or decreasing for time t > t₀, the second theorem is about the complete stability of the trajectory.     

Exact and heuristic approaches for the set cover with pairs problem

This work deals with the set cover with pairs problem (SCPP) which is a generalization of the set cover problem (SCP). In the SCPP the elements have to be covered by specific pairs of objects, instead of a single object. We propose a new mathematical formulation using extended variables that is capable of consistently solve instances with up to 500 elements and 500 objects. We also developed an ILS heuristic which was capable of finding better solutions for several tested instances in less computational time.     

Constrained order packing: comparison of heuristic approaches for a new bin packing problem

Bin packing problems consist of allocating a set of small parts to a set of large bins by minimizing the number of used bins. Although several boundary conditions have been stated in the past, for example conflicts or restrictions on cutting and rotations, we introduce a set of constraints, which lead to a new problem structure. These constraints are motivated by the precast-concrete-part industry and represent requirements on the ordering of parts and their positions, machinery restrictions and due dates. Furthermore, we solve the problem using several heuristic approaches that are based on algorithms for the standard bin packing problem. Therefore, existing concepts are classified and adapted to fit the new problem, including Simulated Annealing, Genetic Algorithms, Tabu Search methods and SubSetSum based search routines. Finally, all proposed algorithms are tested and obtained results are discussed.     

A neural network approach to the vessel dispatching problem

The paper discusses the process of loading, transport and unloading of gravel by inland water transportation. At the loading port, the problem that needs to be solved is the assignment of load barges to pusher tugs for the planned period of one day. However, disturbances of planned schedules are very common. Whenever a disturbance in a daily schedule appears, the dispatcher urgently attempts to mitigate negative effects resulting from the disturbance. Real-time operations limit the amount of time that dispatchers in charge of traffic control have to make decisions and increase the level of stress associated with quick and adequate response. This paper aims to demonstrate the feasibility of a dispatch decision support system that could decrease the work load for the dispatcher and improve the quality of decisions. The proposed neural network with the ability to adapt or learn from examples of decisions can simulate the dispatcher's decision process.     

An application of the neural network energy function to machine sequencing

We apply a neural network approach for solving a one-machine sequencing problem to minimize either single- or multi-objectives, namely the total tardiness, total flowtime, maximimum tardiness, maximum flowtime, and number of tardy jobs. We formulate correspondingly nonlinear integer models, for each of which we derive a quadratic energy function, a neural network, and a system of differential equations. Simulation results based on solving the nonlinear differential equations demonstrate that our approach can effectively solve the sequencing problems to optimality in most cases and near optimality in a few cases. The neural network approach can also be implemented on a parallel computing network, resulting in significant runtime savings over the optimization approach. This paper should not be disseminated without written permission of the authors.     

A model and two heuristic approaches for a forage harvester planning problem: a case study

This work considers a decision problem about orders of owners and routes of smallholdings for a harvester in an agricultural cooperative in which each owner has a proposal about the instant time in which he would like that the machine starts the activity in his land and the different smallholdings of each owner should be processed as a block. A binary linear programming model is introduced in order to reducing costs. Solving the model for actual size instances is computationally burdensome. Hence, we introduce and implement two heuristic algorithms to reduce the computational time. The heuristics are applied to the real case of the cooperative “Os Irmandiños” with a large number of owners and smallholdings. The numerical results show that the heuristics can solve large instances effectively with reasonable computational effort.     

A heuristic approach to a weighted maxmin dispersion problem

In this paper, the nonconvex form of the weighted maxmin dispersionproblem is converted to a form involving the maximization ofconvex functions over a polytope, for which algorithms exist.A heuristic approach is given, together with associated resultson optimality and bounds on loss of optimality.     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay

In this paper, a discrete-time Hopfield neural network with delay is considered. We give some sufficient conditions ensuring the local stability of the equilibrium point for this model. By choosing the delay as a bifurcation parameter, we demonstrated that Neimark–Sacker bifurcation (or Hopf bifurcation for map) would occur when the delay exceeds a critical value. A formula for determining the direction bifurcation and stability of bifurcation periodic solutions is given by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.     

Exact and heuristic solution approaches for the mixed integer setup knapsack problem

We consider a class of knapsack problems that include setup costs for families of items. An individual item can be loaded into the knapsack only if a setup cost is incurred for the family to which it belongs. A mixed integer programming formulation for the problem is provided along with exact and heuristic solution methods. The exact algorithm uses cross decomposition. The proposed heuristic gives fast and tight bounds. In addition, a Benders decomposition algorithm is presented to solve the continuous relaxation of the problem. This method for solving the continuous relaxation can be used to improve the performance of a branch and bound algorithm for solving the integer problem. Computational performance of the algorithms are reported and compared to CPLEX.     

A neural network approach to solve the stable matching problem

In this paper two types of neurons, the maximum selection neuron and the maximum cut-off neuron are introduced. They are used to construct a neural network to represent and solve the stable matching problem. The neural network approach allows the matching to be processed dynamically in a distributed parallel processing environment.