Francisco Baptista Pereira

GVR: A New Genetic Representation for the Vehicle Routing Problem

In this paper we analyse a new evolutionary approach to the vehicle routing problem. We present Genetic Vehicle Representation (GVR), a two-level representational scheme designed to deal in an effective way with all the information that candidate solutions must encode. Experimental results show that this method is both effective and robust, allowing the discovery of new best solutions for some well-known benchmarks.

Multidimensional Knapsack Problem: A Fitness Landscape Analysis

Fitness landscape analysis techniques are used to better understand the influence of genetic representations and associated variation operators when solving a combinatorial optimization problem. Five representations are investigated for the multidimensional knapsack problem. Common mutation operators, such as bit-flip mutation, are employed to generate fitness landscapes. Measures such as fitness distance correlation and autocorrelation are applied to examine the landscapes associated with the tested genetic encodings. Furthermore, additional experiments are made to observe the effects of adding heuristics and local optimization to the representations. Encodings with a strong heuristic bias are more efficient, and the addition of local optimization techniques further enhances their performance.

Bio-inspired Algorithms for the Vehicle Routing Problem

The vehicle routing problem (VRP) is one of the most famous combinatorial optimization problems. In simple terms, the goal is to determine a set of routes with overall minimum cost that can satisfy several geographical scattered demands. Biological inspired computation is a field devoted to the development of computational tools modeled after principles that exist in natural systems. The adoption of such design principles enables the production of problem solving techniques with enhanced robustness and flexibility, able to tackle complex optimization situations. The goal of the volume is to present a collection of state-of-the-art contributions describing recent developments concerning the application of bio-inspired algorithms to the VRP. Over the 9 chapters, different algorithmic approaches are considered and a diverse set of problem variants are addressed. Some contributions focus on standard benchmarks widely adopted by the research community, while others address real-world situations.

An Evolutionary Algorithm for the Global Optimization of Molecular Clusters: Application to Water, Benzene, and Benzene Cation

We have developed an evolutionary algorithm (EA) for the global minimum search of molecular clusters. The EA is able to discover all the putative global minima of water clusters up to (H(2)O)(20) and benzene clusters up to (C(6)H(6))(30). Then, the EA was applied to search for the global minima structures of (C(6)H(6))(n)(+) with n = 2-20, some of which were theoretically studied for the first time. Our results for n = 2-6 are consistent with previous theoretical work that uses a similar interaction potential. Excluding the very symmetric global minimum structure for n = 9, the growth pattern of (C(6)H(6))(n)(+) with n ≥ 7 involves the (C(6)H(6))(2)(+) dimer motif, which is placed off-center in the cluster. Such observation indicates that potentials commonly used in the literature for (C(6)H(6))(n)(+) cannot reproduce the icosahedral-type packing suggested by the available experimental data.

A study on diversity for cluster geometry optimization

Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

On the influence of GVR in vehicle routing

A comparative study is made between a new evolutionary approach for the Vehicle Routing Problem (VRP) and a standard evolutionary model, based on Path Representation. Genetic Vehicle Representation (GVR) is the new two-level representational scheme designed to deal in an effective way with all the information needed by candidate solutions. Experimental results, obtained from a set of VRP instances, show performance improvements when GVR is used.

On the Evolution of Evolutionary Algorithms

In this paper we discuss the evolution of several components of a traditional Evolutionary Algorithm, such as genotype to phenotype mappings and genetic operators, presenting a formalized description of how this can be attained. We then focus on the evolution of mapping functions, for which we present experimental results achieved with a meta-evolutionary scheme.

A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data

We propose a two-step genetic algorithm (GA) to fit potential energy curves to both ab initio and spectroscopic data. In the first step, the GA is applied to fit only the ab initio points; the parameters of the potential so obtained are then used in the second-step GA optimization, where both ab initio and spectroscopic data are included in the fitting procedure. We have tested this methodology for the extended-Rydberg function, but it can be applied to other functions providing they are sufficiently flexible to fit the data. The results for NaLi and Ar2 diatomic molecules show that the present method provides an efficient way to obtain diatomic potentials with spectroscopic accuracy.

On the Use of Different Potential Energy Functions in Rare-Gas Cluster Optimization by Genetic Algorithms: Application to Argon Clusters

We study the effect of the potential energy function on the global minimum structures of argon clusters arising in the optimization performed by genetic algorithms (GAs). We propose a robust and efficient GA which allows for the calculation of all of the putative global minima of Ar(N) (N = 3-78) clusters modeled with four different potentials. Both energetic and structural properties of such minima are compared among each other and with those previously obtained for the Lennard-Jones function. In addition, the possibility of obtaining global minima of one potential through local optimization over the corresponding cluster geometry given by other potentials was associated with some structural parameters. The influence of the contribution from the three-body (Axilrod-Teller-Muto) triple-dipole potential (including or not a damping function to describe its correct behavior at smaller interatomic distances) has also been analyzed.

Designing Efficient Evolutionary Algorithms for Cluster Optimization: A Study on Locality

Cluster geometry optimization is an important problem from the Chemistry area. Hybrid approaches combining evolutionary algorithms and gradient-driven local search methods are one of the most efficient techniques to perform a meaningful exploration of the solution space to ensure the discovery of low energy geometries. Here we performa comprehensive study on the locality properties of this approach to gain insight to the algorithm’s strengths andweaknesses.Theanalysis is accomplished through the application of several static measures to randomly generated solutions in order to establish the main properties of an extended set of mutation and crossover operators. Locality analysis is complemented with additional results obtained from optimization runs. The combination of the outcomes allows us to propose a robust hybrid algorithm that is able to quickly discover the arrangement of the cluster’s particles that correspond to optimal or near-optimal solutions.