Francisco de Toro

A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows

The Capacitated Vehicle Routing Problem with Time Windows is an important combinatorial optimization problem consisting in the determination of the set of routes of minimum distance to deliver goods, using a fleet of identical vehicles with restricted capacity, so that vehicles must visit customers within a time frame. A large number of algorithms have been proposed to solve single-objective formulations of this problem, including meta-heuristic approaches, which provide high quality solutions in reasonable runtimes. Nevertheless, in recent years some authors have analyzed multi-objective variants that consider additional objectives to the distance travelled. This paper considers not only the minimum distance required to deliver goods, but also the workload imbalance in terms of the distances travelled by the used vehicles and their loads. Thus, MMOEASA, a Pareto-based hybrid algorithm that combines evolutionary computation and simulated annealing, is here proposed and analyzed for solving these multi-objective formulations of the VRPTW. The results obtained when solving a subset of Solomons benchmark problems show the good performance of this hybrid approach.

A Simulated Annealing-based parallel multi-objective approach to vehicle routing problems with time windows

The Capacitated Vehicle Routing Problem with Time Windows (VRPTW) consists in determining the routes of a given number of vehicles with identical capacity stationed at a central depot which are used to supply the demands of a set of customers within certain time windows. This is a complex multi-constrained problem with industrial, economic, and environmental implications that has been widely analyzed in the past. This paper deals with a multi-objective variant of the VRPTW that simultaneously minimizes the travelled distance and the imbalance of the routes. This imbalance is analyzed from two perspectives: the imbalance in the distances travelled by the vehicles, and the imbalance in the loads delivered by them. A multi-objective procedure based on Simulated Annealing, the Multiple Temperature Pareto Simulated Annealing (MT-PSA), is proposed in this paper to cope with these multi-objective formulations of the VRPTW. The procedure MT-PSA and an island-based parallel version of MT-PSA have been evaluated and compared with, respectively, sequential and island-based parallel implementations of SPEA2. Computational results obtained on Solomons benchmark problems show that the island-based parallelization produces Pareto-fronts of higher quality that those obtained by the sequential versions without increasing the computational cost, while also producing significant reduction in the runtimes while maintaining solution quality. More specifically, for the most part, our procedure MT-PSA outperforms SPEA2 in the benchmarks here considered, with respect to the solution quality and execution time.

A single front genetic algorithm for parallel multi-objective optimization in dynamic environments

This paper proposes a new parallel evolutionary procedure to solve multi-objective dynamic optimization problems along with some measures to evaluate multi-objective optimization in dynamic environments. These dynamic optimization problems appear in quite different real-world applications with actual socio-economic relevance. In these applications, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online whilst the size of the changes is unknown. Although parallel processing could be very useful in these problems to meet the solution quality requirements and constraints, to date, not many parallel approaches have been reported in the literature. Taking this into account, we introduce a multi-objective optimization procedure for dynamic problems that are based on PSFGA, a parallel evolutionary algorithm previously proposed by us for multi-objective optimization. It uses an island model where a process divides the population among the remaining processes and allows the communication and coordination among the subpopulations in the different islands. The proposed algorithm makes an exclusive use of non-dominating individuals for the selection and variation operator and applies a crowding mechanism to maintain the diversity and the distribution of the solutions in the Pareto front. We also propose a model to understand the benefits of parallel processing in multi-objective problems and the speedup figures obtained in our experiments.

Parallel Processing for Multi-objective Optimization in Dynamic Environments

This paper deals with the use of parallel processing for multi-objective optimization in applications in which the objective functions, the restrictions, and hence also the solutions can change over time. These dynamic optimization problems appear in quite different real-world applications with relevant socio-economic impact. The procedure in this paper is presented based on PSFGA, a parallel evolutionary procedure for multi-objective optimization. It uses a master process that distributes the population among the processors in the system (that evolve their corresponding solutions according to an island model), and collects and adjusts the set of local Pareto fronts found by each processor (this way, the master also allows an implicit communication among islands). Moreover, the procedure exclusively uses non-dominated individuals for the selection and variation, and maintains the diversity of the approximation to the Pareto front by using a strategy based on a crowding distance.

Approaching Dynamic Multi-Objective Optimization Problems by Using Parallel Evolutionary Algorithms

Many real world optimization problems are dynamic. On the other hand, there are many optimization problems whose solutions must optimize several objectives that are in conflict. In these dynamic multi-objective problems the concept of optimum must be redefined, because instead of providing only one optimal solution, the procedures applied to these multi-objective optimization problems should obtain a set of non-dominated solutions (known as Pareto optimal solutions) that change with time. As evolutionary algorithms steer a population of solutions in a concurrent way by making use of cooperative searching techniques, it could be relatively direct to adapt these algorithms to obtain sets of Pareto optimal solutions. This contribution deals with parallel evolutionary algorithms on dynamic multi-objective optimization (DMO) problems. In this kind of problems, the speed of the reaction to changes is a quite important topic in the context of dynamic optimization, and high-performance computing approaches, such as parallel processing, should be applied to meet the given solution constraints and quality requirements.

Performance Measures for Dynamic Multi-Objective Optimization

As most of the performance measures proposed for dynamic optimization algorithms in the literature are only for single objective problems, we propose new measures for dynamic multi-objective problems. Specifically, we give new measures for those problems in which the Pareto fronts are unknown. As these problems are the most common in the industry, our proposed measures constitute an important contribution in order to promote further research on these problems.

Analysis of OpenMP and MPI implementations of meta-heuristics for vehicle routing problems

Graphical abstractDisplay Omitted HighlightsWe parallelize a sequential meta-heuristic based on simulated annealing.The island and master-worker models, and OpenMP and MPI implementations are used.Vehicle routing problems with time windows are used as benchmarks.The performance of multithreading and multi-core processing is analyzed.The different implementation alternatives are statistically compared by using ANOVA. The parallelization of heuristic methods allows the researchers both to explore the solution space more extensively and to accelerate the search process. Nowadays, there is an increasing interest on developing parallel algorithms using standard software components that take advantage of modern microprocessors including several processing cores with local and shared cache memories. The aim of this paper is to show it is possible to parallelize algorithms included in computational software using standard software libraries in low-cost multi-core systems, instead of using expensive high-performance systems or supercomputers. In particular, it is analyzed the benefits provided by master-worker and island parallel models, implemented with MPI and OpenMP software libraries, to parallelize population-based meta-heuristics. The capacitated vehicle routing problem with hard time windows (VRPTW) has been used to evaluate the performance of these parallel strategies. The empirical results for a set of Solomons benchmarks show that the parallel approaches executed on a multi-core processor produce better solutions than the sequential algorithm with respect to both the quality of the solutions obtained and the runtime required to get them. Both MPI and OpenMP parallel implementations are able to obtain better or at least equal solutions (in terms of distance traveled) than the best known ones for the considered benchmark instances.

Multi-objective Optimization Evolutionary Algorithms Applied to Paroxysmal Atrial Fibrillation Diagnosis Based on the k-Nearest Neighbours Classifier

In this paper, multi-objective optimization is applied to determine the parameters for a k-nearest neighbours classifier that has been used in the diagnosis of Paroxysmal Atrial Fibrillation (PAF), in order to get optimal combinations of classification rate, sensibility and specificity. We have considered three different evolutionary algorithms for implementing the multi-objective optimization of parameters: the Single Front Genetic Algorithm (SFGA), an improved version of SFGA, called New Single Front Genetic Algorithm (NSFGA), and the Strength Pareto Evolutionary Algorithm (SPEA). The experimental results and the comparison of the different methods, done by using the hypervolume metric, show that multi-objective optimization constitutes an adequate alternative to combinatorial scanning techniques.

The parallel single front genetic algorithm (PSFGA) in dynamic multi-objective optimization

This paper analyzes the use of the, previously proposed, Parallel Single Front Genetic Algorithm (PSFGA) in applications in which the objective functions, the restrictions, and hence also solutions can change over the time. These dynamic optimization problems appear in quite different real applications with relevant socio-economic impacts. PSFGA uses a master process that distributes the population among the processors in the system (that evolve their corresponding solutions according to an island model), and collects and adjusts the set of local Pareto fronts found by each processor (this way, the master also allows an implicit communication among islands). The procedure exclusively uses non-dominated individuals for the selection and variation, and maintains the diversity of the approximation to the Pareto front by using a strategy based on a crowding distance.

Comparison of Frameworks for Parallel Multiobjective Evolutionary Optimization in Dynamic Problems

In this chapter some alternatives are discussed to take advantage of parallel computers in dynamic multi-objective optimization problems (DMO) using evolutionary algorithms. In DMO problems, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online. Thus, high performance computing approaches, such as parallel processing, should be applied to these problems to meet the quality requirements within the given time constraints. Taking this into account, we describe two generic parallel frameworks for multi-objective evolutionary algorithms. These frameworks are used to compare the parallel processing performance of some multi-objective optimization evolutionary algorithms: our previously proposed algorithms, SFGA and SFGA2, in conjunction with SPEA2 and NSGA-II.We also propose a model to explain the benefits of parallel processing in multi-objective problems and the speedup results observed in our experiments.