Zbigniew J. Czech

Parallel simulated annealing for the vehicle routing problem with time windows

A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is presented. The objective is to find the best possible solutions to some well-known instances of the problem by using parallelism. The empirical evidence indicate that parallel simulated annealing can be applied with success to bicriterion optimization problems.

Parallel Simulated Annealing for Bicriterion Optimization Problems

A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is proposed. It is a complex bicriterion optimization problem in which both the number of vehicles and the total distance traveled by vehicles should be minimized. The aim is to establish the best possible solutions to the well-known instances of the problem by using parallelism. The empirical tests show that parallel simulated annealing can solve effectively bicriterion optimization problems.

Implementing a parallel simulated annealing algorithm

The MPI and OpenMP implementations of the parallel simulated annealing algorithm solving the vehicle routing problem (VRPTW) are presented. The algorithm consists of a number of components which co-operate periodically by exchanging their best solutions found to date. The objective of the work is to explore speedups and scalability of the two implementations. For comparisons the selected VRPTW benchmarking tests are used.

Ant Colony Programming for Approximation Problems

A method of automatic programming, called genetic programming, assumes that the desired program is found by using a genetic algorithm. We propose an idea of ant colony programming in which instead of a genetic algorithm an ant colony algorithm is applied to search for the program. The test results demonstrate that the proposed idea can be used with success to solve the approximation problems.

Three Parallel Algorithms for Simulated Annealing

A vehicle routing problem which reduces to an NP-complete set-partitioning problem is considered. Three parallel algorithms for simulated annealing, i.e. the independent, semi-independent and co-operating searches are investigated. The objective is to improve the accuracy of solutions to the problem by applying parallelism. The accuracy of a solution is meant as its proximity to the optimum solution. The empirical evidence supported by the statistical analysis indicate that co-operation of processes in parallel simulated annealing yields more accurate solutions to the vehicle routing problem as compared to the case when the processes run independently or semi-independently.

Theoretical and practical issues of parallel simulated annealing

Several parallel simulated annealing algorithms with different co-operation schemes are considered. The theoretical analysis of speedups of the algorithms is presented. The outcome of the theoretical analysis was verified by practical experiments whose aim was to investigate the influence of the co-operation of parallel simulated annealing processes on the quality of results. The experiments were performed assuming a constant cost of parallel computations, i.e., searching for solutions was conducted with a given number of processors for a specified period of time. For the experiments a suite of benchmarking tests for the vehicle routing problem with time windows was used.

Frequency of co-operation of parallel simulated annealing processes

A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is considered. The objective is to investigate how the frequency of co-operation of parallel simulated annealing processes influences the quality of solutions to the problem. The quality of a solution is measured by its proximity to the optimum solution.

A Concurrent Implementation of Simulated Annealing and Its Application to the VRPTW Optimization Problem

It is known, that concurrent computing can be applied to heuristic methods (e.g. simulated annealing) for combinatorial optimization to shorten time of computation. This paper presents a communication scheme for message passing environment, tested on the known optimization problem - VRPTW. Application of the scheme allows speed-up without worsening quality of solutions - for one of Solomon’s benchmarking tests the new best solution was found.

Selection Schemes in Evolutionary Algorithms

One of the steps of an evolutionary algorithm is selection which chooses some individuals from a current population as parents to the individuals of the next population. This work focuses on loss of population diversity defined as the proportion of population individuals which are not chosen during selection. Quantifying loss of population diversity is crucial for designing evolutionary algorithms in which the search process is directed through controlling population diversity via parameters of a selection scheme. The aim of this work is to derive closed, approximate formulas which enable to determine loss of population diversity for some selection schemes. The selection schemes under consideration are also compared with respect to effectiveness and ease of controlling population diversity.

Solving bicriterion optimization problems by parallel simulated annealing

A parallel simulated annealing algorithm for solving the vehicle routing problem with time windows (VRPTW) is considered. The VRPTW is a complex bicriterion optimization problem in which both the number of vehicles and the total distance traveled by vehicles should be minimized. The aim is to establish how the number of the cooling stages executed by parallel simulated annealing processes influence the quality of solutions to the problem.