Khalil S. Hindi

New heuristics for one-dimensional bin-packing

Several new heuristics for solving the one-dimensional bin packing problem are presented. Some of these are based on the minimal bin slack (MBS) heuristic of Gupta and Ho. A different algorithm is one based on the variable neighbourhood search metaheuristic. The most effective algorithm turned out to be one based on running one of the former to provide an initial solution for the latter. When tested on 1370 benchmark test problem instances from two sources, this last hybrid algorithm proved capable of achieving the optimal solution for 1329, and could find for 4 instances solutions better than the best known. This is remarkable performance when set against other methods, both heuristic and optimum seeking.

A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit. An effective variable neighbourhood search (VNS) heuristic for this problem is proposed. The neighbourhoods are based on reversing segments of routes (sub-routes) and exchanging segments between routes. Computational results on sixteen standard benchmark problem instances show that the proposed VNS is comparable in terms of solution quality to the best performing published heuristics.

Solving the resource-constrained project scheduling problem by a variable neighbourhood search

Abstract The well-known, challenging problem of resource-constrained project scheduling is addressed. A solution scheme based on variable neighbourhood search is presented. The solution is coded by using activity sequences that are valid in terms of precedence constraints. The sequences are turned into valid active schedules through a serial scheduler. The search of the solution space is carried out via generating valid sequences using two types of move strategy. Much of the power of the solution scheme is attributable to repeatedly employing effective lower bounding and precedence augmentation, both of which serve to reduce the solution space. The effectiveness of the solution scheme is demonstrated through extensive experimentation with a standard set of 2040 benchmark problem instances. The best-known solutions have been improved upon for 48 instances and the best-known lower bounds have also been improved upon for 148 problem instances. The results are inferior to the best-known for a relatively small number of problem instances, but even then the average deviation is very small indeed.

An evolutionary algorithm for resource-constrained project scheduling

The single-mode, single-project, resource-constrained project-scheduling problem is solved by an evolutionary algorithm. The design of this algorithm is presented. Results of a computational study on two sets of benchmark problems, the first consisting of 330 problem instances and the second 2040, are presented. These results show that the proposed algorithm is effective in terms of the number of times it achieves both the best-known solutions and the average error with respect to these solutions, particularly given that the best-known solutions have been compiled from various sources, using a variety of algorithms. Moreover, the computation time requirements are quite modest.

An enumerative heuristic and reduction methods for the assembly line balancing problem

Abstract A new heuristic algorithm and new reduction techniques for the type 1 assembly line balancing problem are presented. The new heuristic is based on the well-known Hoffmann heuristic and builds solutions from both sides of the precedence network to choose the best. The reduction techniques aim at augmenting precedences, conjoining tasks and increasing operation times. The heuristic is tested on its own and also in combination with the reduction techniques. The tests, which are carried out on a well-known benchmark set of problem instances, testify to the efficacy of the combined algorithm, in terms of both solution quality and optimality verification, as well as to its computational efficiency.

Assignment of program modules to processors: A simulated annealing approach

Abstract A simulated annealing approach to the assignment of program modules to processors in a distributed computer system is presented. Modules of a program require certain capacitated computer resources. They also communicate at a given rate. Processors are interconnected by a communication network constituted of various types of links: local area network (LAN), wide area network (WAN) and specialised links. The communication resources are also capacitated. The purpose is to find the assignment of modules to processors such that a measure of performance is optimised, the requirements of each module are met and the capacities of the resources are not violated. Various versions of the problem are identified and formulated. The design of the simulated annealing algorithm to solve the most general version is then described. The results of computational experience are reported.

An effective VNS for the capacitated p-median problem

In the capacitated p-median problem (CPMP), a set of n customers is to be partitioned into p disjoint clusters, such that the total dissimilarity within each cluster is minimized subject to constraints on maximum cluster capacity. Dissimilarity of a cluster is the sum of the dissimilarities between each customer who belongs to the cluster and the median associated with the cluster. An effective variable neighbourhood search heuristic for this problem is proposed. The heuristic is characterized by the use of easily computed lower bounds to assess whether undertaking computationally expensive calculation of the worth of moves, within the neighbourhood search, is necessary. The small proportion of moves that need to be assessed fully are then evaluated by an exact solution of a relatively small subproblem. Computational results on five standard sets of benchmark problem instances show that the heuristic finds all the best-known solutions. For one instance, the previously best-known solution is improved, if only marginally.

A branch-and-bound algorithm for single-machine scheduling with batch delivery and job release times

This paper addresses scheduling a set of jobs with specified release times on a single machine for delivery in batches to customers or to other machines for further processing. This problem is a natural extension of minimizing the sum of flow times in the presence of release time by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvement over an existing dynamic programming algorithm.

An effective heuristic for the CLSP with set-up times

The problem of multi-item, single level, capacitated, dynamic lot-sizing with set-up times (CLSP with set-up times) is considered. The difficulty of the problem compared with its counterpart without set-up times is explained. A lower bound on the value of the objective function is calculated by Lagrangian relaxation with subgradient optimisation. During the process, attempts are made to get good feasible solutions (ie. upper bounds) through a smoothing heuristic, followed by a local search with a variable neighbourhood. Solutions found in this way are further optimised by solving a capacitated transshipment problem. The paper describes the various elements of the solution procedure and presents the results of extensive numerical experimentation.

A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvements over an existing dynamic programming algorithm.