Rafał Skinderowicz

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.

The GPU-based parallel Ant Colony System

Abstract The Ant Colony System (ACS) is, next to Ant Colony Optimization (ACO) and the MAX–MIN Ant System (MMAS), one of the most efficient metaheuristic algorithms inspired by the behavior of ants. In this article we present three novel parallel versions of the ACS for the graphics processing units (GPUs). To the best of our knowledge, this is the first such work on the ACS which shares many key elements of the ACO and the MMAS, but differences in the process of building solutions and updating the pheromone trails make obtaining an efficient parallel version for the GPUs a difficult task. The proposed parallel versions of the ACS differ mainly in their implementations of the pheromone memory. The first two use the standard pheromone matrix, and the third uses a novel selective pheromone memory. Computational experiments conducted on several Traveling Salesman Problem (TSP) instances of sizes ranging from 198 to 2392 cities showed that the parallel ACS on Nvidia Kepler GK104 GPU (1536 CUDA cores) is able to obtain a speedup up to 24.29x vs the sequential ACS running on a single core of Intel Xeon E5-2670 CPU. The parallel ACS with the selective pheromone memory achieved speedups up to 16.85x, but in most cases the obtained solutions were of significantly better quality than for the sequential ACS.

An improved Ant Colony System for the Sequential Ordering Problem

Abstract It is not rare that the performance of one metaheuristic algorithm can be improved by incorporating ideas taken from another. In this article we present how Simulated Annealing (SA) can be used to improve the efficiency of the Ant Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering Problem (SOP). Moreover, we show how the very same ideas can be applied to improve the convergence of a dedicated local search, i.e. the SOP-3-exchange algorithm. A statistical analysis of the proposed algorithms both in terms of finding suitable parameter values and the quality of the generated solutions is presented based on a series of computational experiments conducted on SOP instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed ACS-SA and EACS-SA algorithms often generate solutions of better quality than the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with the proposed SOP-3-exchange-SA local search was able to find 10 new best solutions for the SOP instances from the SOPLIB2006 repository, thus improving the state-of-the-art results as known from the literature. Overall, the best known or improved solutions were found in 41 out of 48 cases.

Ant Colony System with Selective Pheromone Memory for SOP

Ant Colony System (ACS) is a well known metaheuristic algorithm for solving difficult optimization problems inspired by the foraging behaviour of social insects (ants). Artificial ants in the ACS cooperate indirectly through deposition of pheromone trails on the edges of the problem representation graph. All trails comprise a pheromone memory. In this paper we extend the previous work on a novel selective pheromone memory model for the ACS in which pheromone values are stored only for the selected subset of trails. Results of the experiments conducted on several Sequential Ordering Problem (SOP) instances show that it is possible to significantly reduce the ACS memory requirements without impairing the quality of the solutions.

Ant Colony System with a Restart Procedure for TSP

Ant Colony Optimization has proven to be an efficient optimization technique for solving difficult optimization problems. Nonetheless, the convergence of the ACO can still be prohibitively slow. We investigate how the recently proposed Restart Procedure (RP) can be used to improve convergence of the Ant Colony System (ACS) algorithm, which is among the most often applied algorithms from the ACO family. In particular, we present a series of computational experiments to answer the question about how the values of the RP-related parameters influence the convergence of the ACS combined with the RP (ACS-RP). We also show that the ACS-RP achieves significantly better results than the standard ACS within the same computational budget.

Heterarchy in Constructing Decision Trees – Parallel ACDT

In this paper, a novel decision tree construction algorithm that utilizes the Ant Colony Optimization (ACO) is presented. The ACO is a population based metaheuristic inspired by the foraging behavior of real ants. It consists in searching for optimal solutions by considering both local heuristic and accumulated (in the form of pheromone trails) knowledge.

Improving ACO Convergence with Parallel Tempering

Parallel Tempering (PT) is an efficient Monte Carlo simulation method known from statistical physics. We present a novel PT-based Ant Colony Optimization algorithm (PTACO) in which multiple replicas of the Ant Colony System enhanced with a temperature parameter (ACST) are executed in parallel. Based on computational experiments on a set of TSP and ATSP instances we show that the PTACO converges (in terms of solutions quality) significantly faster than the ACS and is competitive to the state-of-the-art Ant Colony Extended algorithm.

Population-Based Ant Colony Optimization for Sequential Ordering Problem

The population-based ant colony optimization (PACO) algorithm uses a pheromone memory model based on a population of solutions stored in a solution archive. Pheromone updates in the PACO are performed only when a solution enters or leaves the archive. Absence of the local pheromone update rule makes the pheromone memory less flexible compared to other ACO algorithms but saves computational time. In this work, we present a novel application of the PACO for solving the sequential ordering problem (SOP). In particular, we investigate how different values of the PACO parameters affect its performance and identify some problems regarding the diversity of solutions stored in the solution archive. A comparison with the state-of-the-art algorithm for the SOP shows that the PACO can be a very competitive tool.

Implementing Population-Based ACO

Population-based ant colony optimization (PACO) is one of the most efficient ant colony optimization (ACO) algorithms. Its strength results from a pheromone memory model in which pheromone values are calculated based on a population of solutions. In each iteration an iteration-best solution may enter the population depending on an update strategy specified. When a solution enters or leaves the population the corresponding pheromone trails are updated. The article shows that the PACO pheromone memory model can be utilized to speed up the process of selecting a new solution component by an ant. Depending on the values of parameters, it allows for an implementation which is not only memory efficient but also significantly faster than the standard approach.

Co-operative, parallel simulated annealing for the VRPTW

The parallel simulated annealing algorithm solving the vehicle routing problem with time windows (VRPTW) is presented. The algorithm consists of a number of processes which co-operate by synchronously exchanging data about their best solutions found so far. The exchange of information is made according to a pre-set communication scheme. The objective of the work is to investigate how the utilization of the data received by a process can affect the accuracy of its solutions to the VRPTW. Performance of the presented parallel algorithm is also considered.