Improved Tabu search heuristics for the dynamic space allocation problem

The dynamic space allocation problem (DSAP) presented in this paper considers the task of assigning items (resources) to locations during a multi-period planning horizon such that the cost of rearranging the items is minimized. Three tabu search heuristics are presented for this problem. The first heuristic is a simple basic tabu search heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic tabu search heuristic. To test the performances of the heuristics, a set of test problems from the literature is used in the analysis. The results show that the tabu search heuristics are efficient techniques for solving the DSAP. More importantly, the proposed tabu search heuristic with diversification/intensification strategies found new best solutions using less computation time for one-half of all the test problems.     

GRASP and hybrid GRASP-Tabu heuristics to solve a maximal covering location problem with customer preference ordering

In this study, a maximal covering location problem is investigated. In this problem, we want to maximize the demand of a set of customers covered by a set of p facilities located among a set of potential sites. It is assumed that a set of facilities that belong to other firms exists and that customers freely choose allocation to the facilities within a coverage radius. The problem can be formulated as a bilevel mathematical programming problem, in which the leader locates facilities in order to maximize the demand covered and the follower allocates customers to the most preferred facility among those selected by the leader and facilities from other firms. We propose a greedy randomized adaptive search procedure (GRASP) heuristic and a hybrid GRASP-Tabu heuristic to find near optimal solutions. Results of the heuristic approaches are compared to solutions obtained with a single-level reformulation of the problem. Computational experiments demonstrate that the proposed algorithms can find very good quality solutions with a small computational burden. The most important feature of the proposed heuristics is that, despite their simplicity, optimal or near-optimal solutions can be determined very efficiently.     

Improved Lagrangian bounds and heuristics for the generalized assignment problem

Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is based on a double decomposable structure of the formulation. A family of greedy heuristics is considered to get Lagrangian based feasible solutions. Numerical results for problem instances with number of agents close to number of tasks are provided.     

Region-rejection based heuristics for the capacitated multi-source Weber problem

A new type of constructive and adaptive heuristics is put forward to generate initial solutions for the capacitated multi-source Weber problem. This technique is based on guiding the search by constructing restricted regions that forbid new locations to be sited too close to the previously found locations. In this work, a restricted region is represented by a circle whose radius is initially set to a fixed value, based on the sparsity of the customers and the number of facilities, and then a scheme that dynamically adjusts the radius at each facility is proposed. A discretisation technique that divides a continuous space into a discrete number of cells while embedding the use of restricted regions within the search is also presented. The experiments show that the proposed region-rejection methods, though simple and easy to understand, provide encouraging results with regard to both solution quality and computational effort. Some future research avenues are also briefly highlighted.     

A hierarchical algorithm for the planar single-facility location routing problem

Location routing problem (LRP) is an important logistical problem that comprises two of the main logistical drivers namely facility location and vehicle routing. In this paper, we focus on the planar single-facility LRP with Euclidean distance where the location of the facility can be anywhere in the space and not restricted to a given set of potential sites only as in the discrete case. A hierarchical heuristic-based method is put forward which continuously takes into account the information from the routing results while systematically improving the location using the end-points of the obtained routes. In addition, some enhancement schemes that include a set of local searches as well as diversification and intensification mechanisms are also incorporated into the search. The proposed method outperformed the existing approaches when tested on the data sets taken from the literature. Our approach produced nine new best results out of the fifteen in the literature besides being relatively robust when compared to the existing methods.     

Solving the maximal covering location problem with heuristic concentration

The metaheuristic heuristic concentration (HC) is applied here to the solution of large instances of the maximal covering location problem with high percentage coverage. In these instances, exact methods may be too cumbersome for practical use, and heuristics can allow faster solution times with near-optimal results. We examined the performance of HC based on its ability to approach the optimal solutions to these problems and the run times of the algorithm compared to LP-IP runtimes. Exact solutions, generated by linear programming and branch and bound, provided a benchmark for comparison when the LP-IP problems could be run to completion. In all cases, HC found solutions with objective values no worse than 0.543% below the best known LP-IP objective value. In several instances, LP-IP runtime ballooned to as much as 38.5 h, while HC took no longer than 1.6 h in any instance. In one particular instance, LP-IP took 38.5 h to terminate, while HC found a near-optimal solution (within 0.306% of optimality) in only 25 min. Furthermore, in 62.5% of the runs, the second stage of HC improved on the first stage 1-opt algorithm.     

New simple and efficient heuristics for the uncapacitated single allocation hub location problem

Hub-and-spoke networks are widely studied in the area of location theory. They arise in several contexts, including passenger airlines, postal and parcel delivery, and computer and telecommunication networks. Hub location problems usually involve three simultaneous decisions to be made: the optimal number of hub nodes, their locations and the allocation of the non-hub nodes to the hubs. In the uncapacitated single allocation hub location problem (USAHLP) hub nodes have no capacity constraints and non-hub nodes must be assigned to only one hub. In this paper, we propose three variants of a simple and efficient multi-start tabu search heuristic as well as a two-stage integrated tabu search heuristic to solve this problem. With multi-start heuristics, several different initial solutions are constructed and then improved by tabu search, while in the two-stage integrated heuristic tabu search is applied to improve both the locational and allocational part of the problem. Computational experiments using typical benchmark problems (Civil Aeronautics Board (CAB) and Australian Post (AP) data sets) as well as new and modified instances show that our approaches consistently return the optimal or best-known results in very short CPU times, thus allowing the possibility of efficiently solving larger instances of the USAHLP than those found in the literature. We also report the integer optimal solutions for all 80 CAB data set instances and the 12 AP instances up to 100 nodes, as well as for the corresponding new generated AP instances with reduced fixed costs.     

Improved core problem based heuristics for the 0/1 multi-dimensional knapsack problem

We consider the 0/1 multi-dimensional knapsack problem and discuss the performances of a new heuristic procedure particularly suitable for a parallel computing environment embedding core problem approaches and a branching scheme based on reduced costs of the corresponding LP relaxation solution value. The proposed approach compared favorably to the recent state of the art procedures available in the literature on the well known OR-Library multi-dimensional knapsack problem benchmarks instances.     

A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application

The assembly flowshop scheduling problem has been addressed recently in the literature. There are many problems that can be modeled as assembly flowshop scheduling problems including queries scheduling on distributed database systems and computer manufacturing. The problem has been addressed with respect to either makespan or total completion time criterion in the literature. In this paper, we address the problem with respect to a due date-based performance measure, i.e., maximum lateness. We formulate the problem and obtain a dominance relation. Moreover, we propose three heuristics for the problem: particle swarm optimization (PSO), Tabu search, and EDD. PSO has been used in the areas of function optimization, artificial neural network training, and fuzzy system control in the literature. In this paper, we show how it can be used for scheduling problems. We have conducted extensive computational experiments to compare the three heuristics along with a random solution. The computational analysis indicates that Tabu outperforms the others for the case when the due dates range is relatively wide. It also indicates that the PSO significantly outperforms the others for difficult problems, i.e., tight due dates. Moreover, for difficult problems, the developed dominance relation helps reduce error by 65%.     

Fuzzy logic based algorithms for maximum covering location problems

This paper concerns a class of maximum covering location problems in networks in uncertain environments. It is assumed that (a) relative weights of demand nodes are either deterministic or imprecise, described by linguistic expressions and (b) potential facility site locations are limited to network nodes. The concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact. The acceptable service distance/travelling times from a facility site to demand nodes are modelled by fuzzy sets. Three new algorithms for choosing the best facility locations are developed which assume that (1) demands at all nodes are equally important, (2) relative weights of demand at nodes are deterministic and (3) weights of demand at nodes are imprecise and described by linguistic terms, respectively. The algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets. It is shown how to extend the proposed algorithms from one-site to multi-site covering problems. Illustrative examples of selecting locations for logistics centres in a distribution company are given.     

A new stochastic approach for a reliable p-hub covering location problem

A hub location problem (HLP) is a fertile research field, in the aspect of interdisciplinary studies, such as transportation, operation research, network design, telecommunication and economics. The location of hub facilities and allocation of non-hub nodes to hubs configure the backbone of HLPs. This study presents a new mathematical model for a reliable HLP by a new stochastic approach to minimize the total transportation cost and obtain maximum flows that the network can carry, when its link capacities are subject to stochastic degradations, as in a form of daily traffic, earthquake, flood, etc. We consider the road capacity reliability as a probability that ensures the maximum network capacity is greater than or equal to the total incoming flow to the network by considering the road capacity as random variable. As a result, this paper assumes that link capacities satisfy in a Truncated Erlang $(\mathit{TErl})$ distribution function. Due to complexity of the HLP, a meta-heuristic algorithm, namely differential evolution (DE) algorithm, is applied on the problem in order to achieve near-optimal solutions. Furthermore, the performance of the proposed algorithm (i.e., DE) is evaluated by the performance of the genetic algorithm (GA) applied on the given problem. Some computational experiments are presented to illustrate the effectiveness of the presented model and proposed algorithm. Finally the conclusion is provided.     

The minimum weighted covering location problem with distance constraints

The objective is to locate undesirable facilities on a network so as to minimize the total demand covered subject to the condition that no two facilities are allowed to be closer than a pre-specified distance. We prove that there exists a dominating location set and that it is a challenging problem to determine the consistency of the distance constraints. We compare several different mathematical formulations to solve the problem. Heuristics with computational experiments are provided.     

Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts

This paper deals with the two-dimensional bin packing problem with conflicts (BPC-2D). Given a finite set of rectangular items, an unlimited number of rectangular bins and a conflict graph, the goal is to find a conflict-free packing of the items minimizing the number of bins used. In this paper, we propose a new framework based on a tree-decomposition for solving this problem. It proceeds by decomposing a BPC-2D instance into subproblems to be solved independently. Applying this decomposition method is not straightforward, since merging partial solutions is hard. Several heuristic strategies are proposed to make an effective use of the decomposition. Computational experiments show the practical effectiveness of our approach.     

An extended continuous maximal covering location problem with facility placement

In this paper we will discuss a formulation of the maximal covering problem when the facilities can be placed anywhere on the set R². A selection of such problems is given. In each case we shall see that the set of locations for facility placement can be reduced to a finite set. Lastly, one of the problems is then solved using an integer program formulation.     

Some heuristics for the consensus ranking problem

In this paper, we propose a consensus ranking function and several heuristics to solve the consensus ranking problem. Empirical testing results of the solution strategies are presented to indicate their solution efficiency.     

Interval-indexed formulation based heuristics for single machine total weighted tardiness problem

In this paper, we solve the single machine total weighted tardiness problem by using integer programming and linear programming based heuristic algorithms. Interval-indexed formulation is used to formulate the problem. We discuss several methods to form the intervals and different post-processing methods. Then, we show how our algorithm can be used to improve a population of a genetic algorithm. We also provide some computational results that show the effectiveness of our algorithm. Many aspects of our heuristic algorithm are quite general and can be applied to other scheduling and combinatorial optimization problems.     

Maximal covering location problem (MCLP) with fuzzy travel times

This paper presents a fuzzy maximal covering location problem (FMCLP) in which travel time between any pair of nodes is considered to be a fuzzy variable. A fuzzy expected value maximization model is designed for such a problem. Moreover, a hybrid algorithm of fuzzy simulation and simulated annealing (SA) is used to solve FMCLP. Some numerical examples are presented, solved and analyzed to show the performance of the proposed algorithm. The results show that the proposed SA finds solutions with objective values no worse than 1.35% below the optimal solution. Furthermore, the simulation-embedded simulated annealing is robust in finding solutions.     

Lower and upper bounds for a two-level hierarchical location problem in computer networks

In this paper a two-level hierarchical model for the location of concentrators and routers in computers networks is presented. Given a set of candidate locations and the capacities of concentrators and routers the problem is to determine how many concentrators and routers should be used, where they should be located and which users to assign to each concentrator and which concentrators to allocate to each router. A Lagrangean relaxation is used to provide lower bounds for this problem, which are tentatively strengthened by incomplete optimization through the use of CPLEX. A tabu search meta-heuristic is then developed. Computational experiments are performed using a set of randomly generated problems.     

Look-ahead heuristics for the dynamic traveling purchaser problem

Given a set of products each with positive discrete demand, and a set of markets selling products at given prices, the traveling purchaser problem (TPP) looks for a tour visiting a subset of markets such that products demand is satisfied at minimum purchasing and traveling costs. In this paper we analyze a dynamic variant of the problem, where quantities may decrease as time goes on. Complete information is assumed on current state of the world, i.e. decision maker knows quantities available for each product in each market at present time and is informed about any consumption event when it occurs. Nevertheless, planner does not have any information on future events. Two groups of heuristics are described and compared. The first group consists of simplified approaches deciding which market to visit next on the basis of some greedy criteria considering only one of the two objective costs. The second one includes heuristics based on a look-ahead approach taking into account both traveling and purchasing costs and inserting some future prediction. Heuristics behavior has been tested on a large set of randomly generated instances under different levels of dynamism.     

Applying two efficient hybrid heuristics for hub location problem with fully interconnected backbone and access networks

This paper considers the design of two-layered networks with fully interconnected backbone and access networks. The problem, a specific application of hub location to network design, is known as fully interconnected network design problem (FINDP). A novel mathematical programming formulation advantageous over an earlier formulation is presented to model the problem. Two hybrid heuristics are proposed to solve the problem, namely SA_VNS and TS_VNS which incorporate a variable neighborhood search (VNS) algorithm into the framework of simulated annealing (SA) and tabu search (TS). The proposed algorithms are able to easily obtain the optimal solutions for 24 small instances existing in the literature in addition to efficiently solve new generated medium and large instances. Results indicate that the proposed algorithms generate high quality solutions in a quite short CPU time.