Tatjana Davidović

Bee colony optimization for the p-center problem

Bee colony optimization (BCO) is a relatively new meta-heuristic designed to deal with hard combinatorial optimization problems. It is biologically inspired method that explores collective intelligence applied by the honey bees during nectar collecting process. In this paper we apply BCO to the p-center problem in the case of symmetric distance matrix. On the contrary to the constructive variant of the BCO algorithm used in recent literature, we propose variant of BCO based on the improvement concept (BCOi). The BCOi has not been significantly used in the relevant BCO literature so far. In this paper it is proved that BCOi can be a very useful concept for solving difficult combinatorial problems. The numerical experiments performed on well-known benchmark problems show that the BCOi is competitive with other methods and it can generate high-quality solutions within negligible CPU times.

Benchmark-problem instances for static scheduling of task graphs with communication delays on homogeneous multiprocessor systems

Scheduling program tasks on processors is at the core of the efficient use of multiprocessor systems. Most task-scheduling problems are known to be NP-Hard and, thus, heuristics are the method of choice in all but the simplest cases. The utilization of acknowledged sets of benchmark-problem instances is essential for the correct comparison and analysis of heuristics. Yet, such sets are not available for several important classes of scheduling problems, including multiprocessor scheduling problem with communication delays (MSPCD) where one is interested in scheduling dependent tasks onto homogeneous multiprocessor systems, with processors connected in an arbitrary way, while explicitly accounting for the time required to transfer data between tasks allocated to different processors. We propose test-problem instances for the MSPCD that are representative in terms of number of processors, type of multiprocessor architecture, number of tasks to be scheduled, and task graph characteristics (task execution times, communication costs, and density of dependencies between tasks). Moreover, we define our task-graph generators in a way appropriate to ensure that the corresponding problem instances obey the theoretical principles recently proposed in the literature.

Bee colony optimization for scheduling independent tasks to identical processors

The static scheduling of independent tasks on homogeneous multiprocessor systems is studied in this paper. This problem is treated by the Bee Colony Optimization (BCO) meta-heuristic. The BCO algorithm belongs to the class of stochastic swarm optimization methods inspired by the foraging habits of bees in nature. To investigate the performance of the proposed method extensive numerical experiments are performed. Our BCO algorithm is able to obtain the optimal value of the objective function in the majority of test examples known from literature. The deviation of non-optimal solutions from the optimal ones in our test examples is at most 2%. The CPU times required to find the best solutions by BCO are significantly smaller than the corresponding times required by the CPLEX optimization solver. Moreover, our BCO is competitive with state-of-the-art methods for similar problems, with respect to both solution quality and running time. The stability of BCO is examined through multiple executions and it is shown that solution deviation is less than 1%.

Permutation-Based Genetic, Tabu, And Variable Neighborhood Search Heuristics For Multiprocessor Scheduling With Communication Delays

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task graph onto a homogeneous multiprocessor system, such that the total execution time (i.e. the time when all tasks are completed) is minimum. The task graph contains precedence relations as well as communication delays (or data transferring time) between tasks if they are executed on different processors. The multiprocessor architecture is assumed to contain identical processors connected in an arbitrary way, which is defined by a symmetric matrix containing minimum distances between every two processors. The solution is represented by a feasible permutation of tasks. In order to obtain the objective function value (i.e. schedule length, makespan), the feasible permutation has to be transformed into the actual schedule by the use of some heuristic method. For solving this NP-hard problem, we develop basic tabu search and variable neighborhood search heuristics, where various types of reduced Or-opt-like neighborhood structures are used for local search. A genetic search approach based on the same solution space is also developed. Comparative computational results on random graphs with up to 500 tasks and 8 processors are reported. On average, it appears that variable neighborhood search outperforms the other metaheuristics. In addition, a detailed performance analysis of both the proposed solution representation and heuristic methods is presented.

Scheduling independent tasks: Bee Colony Optimization approach

The problem of static scheduling of independent tasks on homogeneous multiprocessor systems is studied in this paper. The problem is solved by the Bee Colony Optimization (BCO). The BCO algorithm belongs to the class of stochastic swarm optimization methods. The proposed algorithm is inspired by the foraging habits of bees in the nature. The BCO algorithm was able to obtain the optimal value of objective function in all small to medium size test problems. The CPU times required to find the best solutions by the BCO are acceptable.

Routing of barge container ships by mixed-integer programming heuristics

Abstract We investigate the optimization of transport routes of barge container ships with the objective to maximize the profit of a shipping company. This problem consists of determining the upstream and downstream calling sequence and the number of loaded and empty containers transported between any two ports. We present a mixed integer linear programming (MILP) formulation for this problem. The problem is tackled by the commercial CPLEX MIP solver and improved variants of the existing MIP heuristics: Local Branching, Variable Neighborhood Branching and Variable Neighborhood Decomposition Search. It appears that our implementation of Variable Neighborhood Branching outperforms CPLEX MIP solver both regarding the solution quality and the computational time. All other studied heuristics provide results competitive with CPLEX MIP solver within a significantly shorter amount of time. Moreover, we present a detailed case study transportation analysis which illustrates how the proposed approach can be used by managers of barge shipping companies to make appropriate decisions and solve real life problems.

The bee colony optimization algorithm and its convergence

The bee colony optimization BCO algorithm is a nature-inspired meta-heuristic method for dealing with hard, real-life combinatorial and continuous optimisation problems. It is based on the foraging habits of honeybees and was proposed by Lucic and Teodorovic in 2001. BCO is a simple, but effective meta-heuristic method that has already been successfully applied to various combinatorial optimisation problems in transport, location analysis, scheduling and some other fields. This paper provides theoretical verification of the BCO algorithm by proving some convergence properties. As a result, the gap between successful practice and missing theory is reduced.

MPI Parallelization of Variable Neighborhood Search

Abstract We analyze five parallelization strategies for the Variable Neighborhood Search (VNS) meta–heuristic. They are based on the asynchronous cooperative execution of several threads on different processors. Some of them are adapted from the recent literature, while the others are the newly proposed. We test parallelization on various levels, and we compare centralized and non-centralized information exchange. The implemented parallel searches are applied to benchmark problem instances for Multiprocessor Scheduling Problem with Communication Delays (MSPCD). We achieve not only the improvement of the solution quality but also the reduction in the execution time. The generality of proposed strategies and straightforward implementation make them easy for the application to various difficult combinatorial optimization problems.

MULTIPROCESSOR INTERCONNECTION NETWORKS WITH SMALL TIGHTNESS

Homogeneous multiprocessor systems are usually modelled by undirected graphs. Vertices of these graphs represent the processors, while edges denote the connection links between adjacent processors. Let G be a graph with diameter D, maximum vertex degree Δ, the largest eigenvalue λ1 and m distinct eigenvalues. The products mΔ and (D+1)λ1 are called the tightness of G of the first and second type, respectively. In recent literature it was suggested that graphs with a small tightness of the first type are good models for the multiprocessor interconnection networks. In a previous paper we studied these and some other types of tightness and some related graph invariants and demonstrated their usefulness in the analysis of multiprocessor interconnection networks. We proved that the number of connected graphs with a bounded tightness is finite. In this paper we determine explicitly graphs with tightness values not exceeding 9. There are 69 such graphs and they contain up to 10 vertices. In addition we identify graphs with minimal tightness values when the number of vertices is n = 2,…, 10.

Parallel Local Search to schedule communicating tasks on identical processors

Abstract This paper reports on the analysis of parallelization strategies for Local Search (LS) when the neighborhood size varies throughout the search. The Multiprocessor Scheduling Problem with Communication Delays (MSPCD) is used as benchmark for illustrating the methodology and results. The dynamic load distribution strategy implemented within a supervisor–worker framework is shown to offer the best performance. Experimental results on several sets of instances with up to 500 tasks show excellent speedups (super-linear in most cases) while preserving the quality of the final solution. The proposed parallel LS is incorporated into Multistart Local Search and Variable Neighborhood Search meta-heuristic frameworks to analyze its efficiency in a more complex environment. The comparison between the sequential and parallel versions of each meta-heuristic, using various numbers of processors, shows improvement in the solution quality within proportionally smaller CPU time.