A hybrid algorithm for the Heterogeneous Fleet Vehicle Routing Problem

This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP generalizes the classical Capacitated Vehicle Routing Problem by considering the existence of different vehicle types, with distinct capacities and costs. The objective is to determine the best fleet composition as well as the set of routes that minimize the total costs. The proposed hybrid algorithm is composed by an Iterated Local Search (ILS) based heuristic and a Set Partitioning (SP) formulation. The SP model is solved by means of a Mixed Integer Programming solver that interactively calls the ILS heuristic during its execution. The developed algorithm was tested in benchmark instances with up to 360 customers. The results obtained are quite competitive with those found in the literature and new improved solutions are reported.     

Hybrid scatter search and path relinking for the capacitated p-median problem

In this paper we propose heuristic algorithms for the capacitated p-median problem. In the first one solutions are obtained with Scatter Search whereas the second algorithm uses Path Relinking. A third approach that combines Path Relinking with Scatter Search is also analyzed. The GRASP methodology is used to generate the initial Reference Set both for Scatter Search and Path Relinking. Computational experiments have been carried out with different data sets in order to evaluate the performance of the approaches. In general, Scatter Search outperforms Path Relinking, but the use of Path Relinking prior to Scatter Search has shown to enhance the performance of Scatter Search, specially in terms of the computation times required, due to the improvement of the initial Reference Set. The obtained results, that have been compared with previous approaches, show the efficiency of the methods both in terms of the quality of the solutions found and of the required computation times, even for very large instances.     

Hybrid biobjective evolutionary algorithms for the design of a hospital waste management network

Colombian environmental authorities are exploring new alternatives for improving the disposal of hospital waste generated in the Department of Boyacá (Colombia). To design this hospital waste management network we propose a biobjective obnoxious facility location problem (BOOFLP) that deals with the existing tradeoff between a low-cost operating network and the negative effect on the population living near the waste management facilities. To solve the BOOFLP we propose a hybrid approach that combines a multiobjective evolutionary algorithm (NSGA II) with a mixed-integer program. The algorithms are compared against the Noninferior Set Estimation (NISE) method and tested on data from Boyacá’s hospital waste management network and publicly available instances.     

Maximal- and minimal symmetric solutions of fully fuzzy linear systems

In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system (FFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a FFLS (in the present paper, we assumed that the 1-cut of a FFLS is a crisp linear system or equivalently, the matrix coefficient and right hand side have triangular shapes), then some unknown symmetric spreads are allocated to each row of a 1-cut of a FFLS. So, after some manipulations, the original FFLS is transformed to solving 2n linear equations to find the symmetric spreads. However, our method always give us a fuzzy number vector solution. Moreover, using the proposed method leads to determining the maximal- and minimal symmetric solutions of the FFLS which are placed in a Tolerable Solution Set and a Controllable Solution Set, respectively. However, the obtained solutions could be interpreted as bounded symmetric solutions of the FFLS which are useful for a large number of multiplications existing between two fuzzy numbers. Finally, some numerical examples are given to illustrate the ability of the proposed method.     

Genetic algorithms for the bus driver scheduling problem: a case study

This paper describes an application of genetic algorithms to the bus driver scheduling problem. The application of genetic algorithms extends the traditional approach of Set Covering/Set Partitioning formulations, allowing the simultaneous consideration of several complex criteria. The genetic algorithm is integrated in a DSS but can be used as a very interactive tool or a stand-alone application. It incorporates the user's knowledge in a quite natural way and produces solutions that are almost directly implemented by the transport companies in their operational planning processes. Computational results with airline and bus crew scheduling problems from real world companies are presented and discussed.     

A probabilistic greedy search algorithm for combinatorial optimisation with application to the set covering problem

We present a probabilistic greedy search method for combinatorial optimisation problems. This approach is implemented and evaluated for the Set Covering Problem (SCP) and shown to yield a simple, robust, and quite fast heuristic. Tests performed on a large set of benchmark instances with up to 1000 rows and 10?000 columns show that the algorithm consistently yields near-optimal solutions.     

K-PPM: A new exact method to solve multi-objective combinatorial optimization problems

In this paper we propose an exact method able to solve multi-objective combinatorial optimization problems. This method is an extension, for any number of objectives, of the 2-Parallel Partitioning Method (2-PPM) we previously proposed. Like 2-PPM, this method is based on splitting of the search space into several areas, leading to elementary searches. The efficiency of the proposed method is evaluated using a multi-objective flow-shop problem.     

Master physician scheduling problem

We study a real-world problem arising from the operations of a hospital service provider, which we term the master physician scheduling problem. It is a planning problem of assigning physicians’ full range of day-to-day duties (including surgery, clinics, scopes, calls, administration) to the defined time slots/shifts over a time horizon, incorporating a large number of constraints and complex physician preferences. The goals are to satisfy as many physicians’ preferences and duty requirements as possible while ensuring optimum usage of available resources. We propose mathematical programming models that represent different variants of this problem. The models were tested on a real case from the Surgery Department of a local government hospital, as well as on randomly generated problem instances. The computational results are reported together with analysis on the optimal solutions obtained. For large-scale instances that could not be solved by the exact method, we propose a heuristic algorithm to generate good solutions.     

A Branch-and-Price Algorithm for the Capacitated Arc Routing Problem with Stochastic Demands

We address the Capacitated Arc Routing Problem with Stochastic Demands (CARPSD), which we formulate as a Set Partitioning Problem. The CARPSD is solved by a Branch-and-Price algorithm, which we apply without graph transformation. The demand’s stochastic nature is incorporated into the pricing problem. Computational results are reported.     

Non Delayed Relax-and-Cut Algorithms

Attempts to allow exponentially many inequalities to be candidates to Lagrangian dualization date from the early 1980's. In this paper, the term Relax-and-Cut, introduced elsewhere, is used to denote the whole class of Lagrangian Relaxation algorithms where Lagrangian bounds are attempted to be improved by dynamically strengthening relaxations with the introduction of valid constraints. An algorithm in that class, denoted here Non Delayed Relax-and-Cut, is described in detail, together with a general framework to obtain feasible integral solutions. Specific implementations of NDRC are presented for the Steiner Tree Problem and for a Cardinality Constrained Set Partitioning Problem.     

Discrete location for bundled demand points

This paper considers a discrete location problem where the demand points are grouped. We propose a formulation, an enforcement for it, and an associated Lagrangian relaxation, and then we build feasible solutions to the problem from the optimal solutions to the relaxed subproblems. Valid inequalities for the formulation are also identified and added to the set of relaxed constraints. This method produces good feasible solutions and enables us to address large instances of the problem. Computational experiments have been performed with benchmark instances from the literature on related problems.     

General variable neighborhood search for the uncapacitated single allocation <Emphasis Type="Italic">p</Emphasis>-hub center problem

In this paper we propose a general variable neighborhood search heuristic for solving the uncapacitated single allocation p-hub center problem (USApHCP). For the local search step we develop a nested variable neighborhood descent strategy. The proposed approach is tested on benchmark instances from the literature and found to outperform the state-of-the-art heuristic based on ant colony optimization. We also test our heuristic on large scale instances that were not previously considered as test instances for the USApHCP. Moreover, exact solutions were reached by our GVNS for all instances where optimal solutions are known.     

Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponential-time algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions.     

A mathematical formulation and complexity considerations for the blocks relocation problem

The blocks relocation problem (BRP) may be defined as follows: given a set of homogeneous blocks stored in a two-dimensional stock, which relocations are necessary to retrieve the blocks from the stock in a predefined order while minimizing the number of those relocations? In this paper, we first prove NP-hardness of the BRP as well as a special case, closing open research questions. Moreover, we propose different solution approaches. First, a mathematical model is presented that provides optimal solutions to the general BRP in cases where instances are small. To overcome such limitation, some realistic assumption taken from the literature is introduced, leading to the definition of a binary linear programming model. In terms of computational time, this approach is reasonably fast to be used to solve medium-sized instances. In addition, we propose a simple heuristic based upon a set of relocation rules. This heuristic is used to generate “good” quality solutions for larger instances in very short computational time, and, consequently, is proposed for tackling problem instances where solutions are required (almost) immediately. Solution quality of the heuristic is measured against optimal solutions obtained using a state-of-the-art commercial solver and both of them are compared with reference results from literature.     

Computing the metric dimension of graphs by genetic algorithms

In this paper we consider the NP-hard problem of determining the metric dimension of graphs. We propose a genetic algorithm (GA) that uses the binary encoding and the standard genetic operators adapted to the problem. The feasibility is enforced by repairing the individuals. The overall performance of the GA implementation is improved by a caching technique. Since the metric dimension problem up to now has been considered only theoretically, standard test instances for this problem do not exist. For that reason, we present the results of the computational experience on several sets of test instances for other NP-hard problems: pseudo boolean, crew scheduling and graph coloring. Testing on instances with up to 1534 nodes shows that GA relatively quickly obtains approximate solutions. For smaller instances, GA solutions are compared with CPLEX results. We have also modified our implementation to handle theoretically challenging large-scale classes of hypercubes and Hamming graphs. In this case the presented approach reaches optimal or best known solutions for hypercubes up to 131072 nodes and Hamming graphs up to 4913 nodes.     

Scatter search for the single source capacitated facility location problem

This paper considers the Single Source Capacitated Facility Location Problem (SSCFLP). We propose a Scatter Search approach to provide upper bounds for the optimal solution of the problem. The proposed approach uses GRASP to initialize the Reference Set. Solutions of the Reference Set are combined using a procedure that consists of two phases: (1) the initialization phase and (2) the improvement phase. During the initialization phase each client is assigned to an open facility to obtain a solution that is then improved with the improvement phase. Also, a tabu search algorithm is applied. In order to evaluate the proposed approach we use different sets of test problems. According to the results obtained we observe that the method provides good quality solutions with reasonable computational effort.     

A memetic algorithm for the team orienteering problem

The team orienteering problem (TOP) is a generalization of the orienteering problem. A limited number of vehicles is available to visit customers from a potential set. Each vehicle has a predefined running-time limit, and each customer has a fixed associated profit. The aim of the TOP is to maximize the total collected profit. In this paper we propose a simple hybrid genetic algorithm using new algorithms dedicated to the specific scope of the TOP: an Optimal Split procedure for chromosome evaluation and local search techniques for mutation. We have called this hybrid method a memetic algorithm for the TOP. Computational experiments conducted on standard benchmark instances clearly show our method to be highly competitive with existing ones, yielding new improved solutions in at least 5 instances.     

Scatter search for the cutwidth minimization problem

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges is minimized. This NP-hard problem has applications in network scheduling, automatic graph drawing and information retrieval. We propose a heuristic method based on the Scatter Search (SS) methodology for finding approximate solutions to this optimization problem. This metaheuristic explores solution space by evolving a set of reference points. Our SS method is based on a GRASP constructive algorithm, a local search strategy based on insertion moves and voting-based combination methods. We also introduce a new measure to control the diversity in the search process. Empirical results with 252 previously reported instances indicate that the proposed procedure compares favorably to previous metaheuristics for this problem, such as Simulated Annealing and Evolutionary Path Relinking.     

A New Hybrid Generalized Proximal Point Algorithm for Variational Inequality Problems

In this paper, we propose a modified Bregman-function-based proximal point algorithm for solving variational inequality problems. The algorithm adopts a similar constructive approximate criterion as the one developed by Solodov and Svaiter (Set Valued Analysis 7 (1999) 323) for solving the classical proximal subproblems. Under some suitable conditions, we can get an approximate solution satisfying the accuracy criterion via a single Newton-type step. We obtain the Fejér monotonicity to solutions of VIP for paramonotone operators. Some preliminary computational results are also reported to illustrate the method.