A biased random-key genetic algorithm for the Steiner triple covering problem

We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A ₄₀₅ and A ₇₂₉ have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size.     

A biased random-key genetic algorithm for the project scheduling problem with flexible resources

In this paper, we investigate a resource-constrained project scheduling problem with flexible resources. This is an \(\mathcal {NP}\)-hard combinatorial optimization problem that consists of scheduling a set of activities requiring specific resource units of several skills. The goal is to minimize the makespan of the project. We propose a biased random-key genetic algorithm for computing feasible solutions for the referred problem. We study different decoding mechanisms: an already existing method in the literature, a new adapted serial scheduling generation scheme, and a combination of both. The new procedure is tested using a set of benchmark instances of the problem. The results provide strong evidence that the new heuristic is robust and yields high-quality feasible solutions.     

A biased random-key genetic algorithm for road congestion minimization

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms.     

A biased random-key genetic algorithm for routing and wavelength assignment

The problem of routing and wavelength assignment in wavelength division multiplexing optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned different wavelengths. This problem was shown to be NP-hard when the objective is to minimize the total number of wavelengths used. We propose a genetic algorithm with random keys for routing and wavelength assignment with the goal of minimizing the number of different wavelengths used in the assignment. This algorithm extends the best heuristic in the literature by embedding it into an evolutionary framework. Computational results show that the new heuristic improves the state-of-the-art algorithms in the literature.     

An improved Benders decomposition algorithm for the tree of hubs location problem

The tree of hubs location problem is a particularly hard variant of the so called hub location problems. When solving this problem by a Benders decomposition approach, it is necessary to deal with both optimality and feasibility cuts. While modern implementations of the Benders decomposition method rely on Pareto-optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems, a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems. The proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature.     

A random-key genetic algorithm for the generalized traveling salesman problem

The generalized traveling salesman problem is a variation of the well-known traveling salesman problem in which the set of nodes is divided into clusters; the objective is to find a minimum-cost tour passing through one node from each cluster. We present an effective heuristic for this problem. The method combines a genetic algorithm (GA) with a local tour improvement heuristic. Solutions are encoded using random keys, which circumvent the feasibility problems encountered when using traditional GA encodings. On a set of 41 standard test problems with symmetric distances and up to 442 nodes, the heuristic found solutions that were optimal in most cases and were within 1% of optimality in all but the largest problems, with computation times generally within 10 seconds. The heuristic is competitive with other heuristics published to date in both solution quality and computation time.     

A tree search algorithm for the multi-commodity location problem

The multi-commodity location problem is an extension of the simple plant location problem. The problem is to decide on locations of facilities to meet customer demands for several commodities in such a way that total fixed plus variable costs are minimized. Only one commodity may be supplied from any location.In this paper a primal and a dual heuristic for producing good bounds are presented. A method of improving these bounds by using a new Lagrangean relaxation for the problem is also presented. Computational results with problems taken from the literature are provided.     

A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem

Journal of Heuristics - In this paper, we propose a method to solve a bi-objective variant of the well-studied traveling thief problem (TTP). The TTP is a multi-component problem that combines two...     

Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm

Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we address the problem of finding all roots of a system of equations. Our method makes use of a biased random-key genetic algorithm (BRKGA). Given a nonlinear system, we construct a corresponding optimization problem, which we solve multiple times, making use of a BRKGA, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on seven nonlinear equations systems with multiple roots from the literature.     

A biased random key genetic algorithm applied to the electric distribution network reconfiguration problem

This work presents a biased random-key genetic algorithm (BRKGA) to solve the electric distribution network reconfiguration problem (DNR). The DNR is one of the most studied combinatorial optimization problems in power system analysis. Given a set of switches of an electric network that can be opened or closed, the objective is to select the best configuration of the switches to optimize a given network objective while at the same time satisfying a set of operational constraints. The good performance of BRKGAs on many combinatorial optimization problems and the fact that it has never been applied to solve DNR problems are the main motivation for this research. A BRKGA is a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. Solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval (0,1), thus enabling an indirect search of the solution inside a proprietary search space. The genetic operators do not need to be modified to generate only feasible solutions, which is an exclusive task of the decoder of the problem. Tests were performed on standard distribution systems used in DNR studies found in the technical literature and the performance and robustness of the BRKGA were compared with other GA implementations.     

A search tree algorithm for plant location problems

This paper deals with the classical plant location problem, by introducing a new algorithm based on a ranking procedure of all the possible combinations of plant locations. The ranking is obtained by introducing a properly defined search tree and by exploiting its structural properties, so that the algorithm suitably combines a search procedure on the tree with a ranking method. The number of subproblems to be examined is greatly reduced by the use of a stopping rule and a lower bound. The lower bound is given by the value of the objective function of a dual feasible solution for the transportation problem associated to each combination. Computational results for a set of real size problems with different data structures are finally discussed.     

A branch-and-cut algorithm for the plant-cycle location problem

The Plant-Cycle Location Problem (PCLP) is defined on a graph G=(I∪J, E), where I is the set of customers and J is the set of plants. Each customer must be served by one plant, and the plant must be opened to serve customers. The number of customers that a plant can serve is limited. There is a cost of opening a plant, and of serving a customer from an open plant. All customers served by a plant are in a cycle containing the plant, and there is a routing cost associated to each edge of the cycle. The PCLP consists in determining which plants to open, the assignment of customers to plants, and the cycles containing each open plant and its customers, minimizing the total cost. It is an NP-hard optimization problem arising in routing and telecommunications. In this article, the PCLP is formulated as an integer linear program, a branch-and-cut algorithm is developed, and computational results on real-world data and randomly generated instances are presented. The proposed approach is able to find optimal solutions of random instances with up to 100 customers and 100 potential plants, and of instances on real-world data with up to 120 customers and 16 potential plants.     

A multi-objective genetic algorithm for a bi-objective facility location problem with partial coverage

In this study, we present a bi-objective facility location model that considers both partial coverage and service to uncovered demands. Due to limited number of facilities to be opened, some of the demand nodes may not be within full or partial coverage distance of a facility. However, a demand node that is not within the coverage distance of a facility should get service from the nearest facility within the shortest possible time. In this model, it is assumed that demand nodes within the predefined distance of opened facilities are fully covered, and after that distance the coverage level decreases linearly. The objectives are defined as the maximization of full and partial coverage, and the minimization of the maximum distance between uncovered demand nodes and their nearest facilities. We develop a new multi-objective genetic algorithm (MOGA) called modified SPEA-II (mSPEA-II). In this method, the fitness function of SPEA-II is modified and the crowding distance of NSGA-II is used. The performance of mSPEA-II is tested on randomly generated problems of different sizes. The results are compared with the solutions of the most well-known MOGAs, NSGA-II and SPEA-II. Computational experiments show that mSPEA-II outperforms both NSGA-II and SPEA-II.     

A polynomial algorithm for the multicriteria cent-dian location problem

Given a network with several weights per node and several lengths per edge, we address the problem of locating a facility on the network such that the convex combinations of the center and median objective functions are minimized. Since we consider several weights and several lengths, various objective functions should be minimized, and hence we have to solve a multicriteria cent-dian location problem. A polynomial algorithm to characterize the efficient location point set on the network is developed. Furthermore, this model can generalize other problems such as the multicriteria center problem and the multicriteria median problem. Computing time results on random planar networks considering different combinations of weights and lengths are reported, which strengthen the polynomial complexity of the procedure.     

A fast algorithm for the rectilinear distance location problem

In this paper, we consider the rectilinear distance location problem with box constraints (RDLPBC) and we show that RDLPBC can be reduced to the rectilinear distance location problem (RDLP). A necessary and sufficient condition of optimality is provided for RDLP. A fast algorithm is presented for finding the optimal solution set of RDLP. Global convergence of the method is proved by a necessary and sufficient condition. The new proposed method is provably more efficient in finding the optimal solution set. Computational experiments highlight the magnitude of the theoretical efficiency.     

A branch-and-price algorithm for the capacitated facility location problem

The capacitated facility location problem (CFLP) is a well-known combinatorial optimization problem with applications in distribution and production planning. It consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs. A number of solution approaches based on Lagrangean relaxation and subgradient optimization has been proposed for this problem. Subgradient optimization does not provide a primal (fractional) optimal solution to the corresponding master problem. However, in order to compute optimal solutions to large or difficult problem instances by means of a branch-and-bound procedure information about such a primal fractional solution can be advantageous. In this paper, a (stabilized) column generation method is, therefore, employed in order to solve a corresponding master problem exactly. The column generation procedure is then employed within a branch-and-price algorithm for computing optimal solutions to the CFLP. Computational results are reported for a set of larger and difficult problem instances.     

A modified Weiszfeld algorithm for the Fermat-Weber location problem

This paper gives a new, simple, monotonically convergent, algorithm for the Fermat-Weber location problem, with extensions covering more general cost functions. Received: September 1999 / Accepted: January 2001?Published online April 12, 2001     

A tree search algorithm for the crew scheduling problem

In this paper we consider the crew scheduling program, that is the problem of assigning K crews to N tasks with fixed start and finish times such that each crew does not exceed a limit on the total time it can spend working.A zero-one integer linear programming formulation of the problem is given, which is then relaxed in a lagrangean way to provide a lower bound which is improved by subgradient optimisation. Finally a tree search procedure incorporating this lower bound is presented to solve the problem to optimality.Computational results are given for a number of randomly generated test problems involving between 50 and 500 tasks.