Some heuristic algorithms for total tardiness minimization in a flowshop with blocking

The flowshop scheduling problem with blocking in-process is addressed in this paper. In this environment, there are no buffers between successive machines; therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. Heuristic approaches are proposed to minimize the total tardiness criterion. A constructive heuristic that explores specific characteristics of the problem is presented. Moreover, a GRASP-based heuristic is proposed and coupled with a path relinking strategy to search for better outcomes. Computational tests are presented and the comparisons made with an adaptation of the NEH algorithm and with a branch-and-bound algorithm indicate that the new approaches are promising.     

An optimization approach applied to the optimal stratification problem

A new optimization algorithm is presented to solve the stratification problem. Assuming the number L of strata and the total sample size n are fixed, we obtain strata boundaries by using an objective function associated with the variance. In this problem, strata boundaries must be determined so that the elements in each stratum are more homogeneous among themselves. To produce more homogeneous strata, this paper proposes a new algorithm that uses the Greedy Randomized Adaptive Search Procedure (GRASP) methodology. Computational results are presented for a set of problems, with the application of the new algorithm and some algorithms from literature.     

Multiple phase neighborhood Search—GRASP based on Lagrangean relaxation, random backtracking Lin–Kernighan and path relinking for the TSP

In this paper, a new modified version of Greedy Randomized Adaptive Search Procedure (GRASP), called Multiple Phase Neighborhood Search—GRASP (MPNS-GRASP), is proposed for the solution of the Traveling Salesman Problem. In this method, some procedures have been included to the classical GRASP algorithm in order to improve its performance and to cope with the major disadvantage of GRASP which is that it does not have a stopping criterion that will prevent the algorithm from spending time in iterations that give minor, if any, improvement in the solution. Thus, in MPNS-GRASP a stopping criterion based on Lagrangean Relaxation and Subgradient Optimization is proposed. Also, a different way for expanding the neighborhood search is used based on a new strategy, the Circle Restricted Local Search Moves strategy. A new variant of the Lin-Kernighan algorithm, called Random Backtracking Lin-Kernighan that helps the algorithm to diversify the search in non-promising regions of the search space is used in the Expanding Neighborhood Search phase of the algorithm. Finally, a Path Relinking Strategy is used in order to explore trajectories between elite solutions. The proposed algorithm is tested on numerous benchmark problems from TSPLIB with very satisfactory results.     

Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona

Reverse logistics problems arising in municipal waste management are both wide-ranging and varied. The usual collection system in UE countries is composed of two phases. First, citizens leave their refuse at special collection areas where different types of waste (glass, paper, plastic, organic material) are stored in special refuse bins. Subsequently, each type of waste is collected separately and moved to its final destination (a recycling plant or refuse dump). The present study focuses on the problem of locating these collection areas. We establish the relationship between the problem, the set covering problem and the MAX-SAT problem and then go on to develop a genetic algorithm and a GRASP heuristic to, respectively, solve each formulation. Finally, the quality of the algorithms is tested in a computational experience with real instances from the metropolitan area of Barcelona, as well as a reduced set of set covering instances from the literature.     

A Grasp for Aircraft Routing in Response to Groundings and Delays

This paper presents a greedy randomized adaptive search procedure (GRASP) to reconstruct aircraft routings in response to groundings and delays experienced over the course of the day. Whenever the schedule is disrupted, the immediate objective of the airlines is to minimize the cost of reassigning aircraft to flights taking into account available resources and other system constraints. Associated costs are measured by flight delays and cancellations.In the procedure, the neighbors of an incumbent solution are generated and evaluated, and the most desirable are placed on a restricted candidate list. One is selected randomly and becomes the incumbent. The heuristic is polynomial with respect to the number of flights and aircraft. This is reflected in our computational experience with data provided by Continental Airlines. Empirical results demonstrate the ability of the GRASP to quickly explore a wide range of scenarios and, in most cases, to produce an optimal or near-optimal solution.     

A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem

A Greedy Randomized Adaptive Search Procedure (GRASP) is a randomized heuristic that has produced high quality solutions for a wide range of combinatorial optimization problems. The NP-complete Feedback Vertex Set (FVS) Problem is to find the minimum number of vertices that need to be removed from a directed graph so that the resulting graph has no directed cycle. The FVS problem has found applications in many fields, including VLSI design, program verification, and statistical inference. In this paper, we develop a GRASP for the FVS problem. We describe GRASP construction mechanisms and local search, as well as some efficient problem reduction techniques. We report computational experience on a set of test problems using three variants of GRASP.     

The planning of cycle trips in the province of East Flanders

Traditional route planners assist in finding the shortest or fastest route from one place to another. This paper presents a novel approach to path finding in a directed graph, namely a target distance, motivated by the problem that a recreational cyclist deals with when searching a nice route of a certain length. The problem is defined as a variant of the arc orienteering problem (AOP), a new combinatorial optimisation problem in which the score of a route in a directed graph has to be maximised by visiting arcs, while each arc can be visited at most once and the total cost of the route should not exceed a predefined cost. The contribution of this paper is threefold: (1) a mathematical model of the AOP is provided, (2) a metaheuristic method that solves AOP instances to near optimality in 1 s of execution time, is proposed and evaluated, and (3) two real-life applications of the method are presented. An on-line cycle route planning application offers personalised cycle routes based on user preferences, and an SMS service provides cyclists “in the field” with routes on demand.