Valentino Santucci

Algebraic Differential Evolution Algorithm for the Permutation Flowshop Scheduling Problem With Total Flowtime Criterion

This paper introduces an original algebraic approach to differential evolution (DE) algorithms for combinatorial search spaces. An abstract algebraic differential mutation for generic combinatorial spaces is defined by exploiting the concept of a finitely generated group. This operator is specialized for the permutations space by means of an original randomized bubble sort algorithm. Then, a discrete DE algorithm is derived for permutation problems and it is applied to the permutation flowshop scheduling problem with the total flowtime criterion. Other relevant components of the proposed algorithm are: a crossover operator for permutations, a novel biased selection strategy, a heuristic-based initialization, and a memetic restart procedure. Extensive experimental tests have been performed on a widely accepted benchmark suite in order to analyze the dynamics of the proposed approach and to compare it with the state-of-the-art algorithms. The experimental results clearly show that the proposed algorithm reaches state-of-the-art performances and, most remarkably, it is able to find some new best known results. Furthermore, the experimental analysis on the impact of the algorithmic components shows that the two main contributions of this paper, i.e., the discrete differential mutation and the biased selection operator, greatly contribute to the overall performance of the algorithm.

Community of scientist optimization: An autonomy oriented approach to distributed optimization

A novel optimization paradigm, called Community of Scientists Optimization (CoSO), is presented in this paper. The approach is inspired to the behaviour of a community of scientists interacting, pursuing for research results and foraging the funds needed to held their research activities. The CoSO metaphor can be applied to general optimization domains, where optimal solutions emerge from the collective behaviour of a distributed community of interacting autonomous entities. The CoSO framework presents analogies and remarkable differences with other evolutionary optimization approaches: swarm behaviour, foraging and selection mechanism based on research funds competition, dynamically evolving multicapacity communication channels realized by journals and evolving population size regulated by research management strategies. Experiments and comparisons on benchmark problems show the effectiveness of the approach for numerical optimization. CoSO, with the design of appropriate foraging and competition strategies, also represents a great potential as a general meta-heuristic for applications in non-numerical and agent-based domains.

A Differential Evolution Algorithm for the Permutation Flowshop Scheduling Problem with Total Flow Time Criterion

In this paper a new discrete Differential Evolution algorithm for the Permutation Flowshop Scheduling Problem with the total flowtime criterion is proposed. The core of the algorithm is the distance-based differential mutation operator defined by means of a new randomized bubble sort algorithm. This mutation scheme allows the Differential Evolution to directly navigate the permutations search space. Experiments were held on a well known benchmark suite and the results show that our proposal outperforms state-of-the-art algorithms on the majority of the problems.

Linear Ordering Optimization with a Combinatorial Differential Evolution

In this work, the Linear Ordering Problem (LOP) has been approached using a discrete algebraic-based Differential Evolution for the Linear Ordering Problem (LOP). The search space of LOP is composed by permutations of objects, thus it is possible to use some group theoretical concepts and methods. Indeed, the proposed algorithm is a combinatorial Differential Evolution scheme designed by exploiting the group structure of the LOP solutions in order to mimic the classical Differential Evolution behavior observed in continuous spaces. In particular, the proposed differential mutation operator allows to obtain both scaled and extended differences among LOP solutions represented by permutations. The performances have been evaluated over widely known LOP benchmark suites and have been compared to the state-of-the-art results.

Solving permutation flowshop scheduling problems with a discrete differential evolution algorithm

In this paper a new discrete Differential Evolution algorithm for the Permutation Flowshop Scheduling Problem with the total flowtime and makespan criteria is proposed. The core of the algorithm is the distance-based differential mutation operator defined by means of a new randomized bubble sort algorithm. This mutation scheme allows the Differential Evolution to directly navigate the permutations search space. Experiments were held on a well known benchmarks suite and they show that the proposal reaches very good performances compared to other state-of-the-art algorithms. The results are particularly satisfactory on the total flowtime criterion where also new upper bounds that improve on the state-of-the-art have been found.

An Algebraic Differential Evolution for the Linear Ordering Problem

In this paper we propose a discrete algebraic-based Differential Evolution for the Linear Ordering Problem (LOP). The search space of LOP is composed by permutations of objects, thus it is possible to use some group theoretical concepts and methods. Indeed, the proposed algorithm is a fully discrete Differential Evolution scheme and has been designed by exploiting the group structure of LOP solutions in order to mimic the classical Differential Evolution behavior observed in continuous numerical spaces. The performances have been evaluated over widely known LOP benchmark suites and have been compared to the state-of-the-art results.

Asynchronous Differential Evolution

This paper introduces the Asynchronous Differential Evolution (ADE) scheme which generalizes the classical Differential Evolution (DE) approach along the dimension of Synchronization Degree (SD). SD regulates the synchrony of the evolution of the current population, i.e. how fast it is replaced by the newly generated population. The definition of the ADE scheme is given and different synchronization strategies are discussed. The introduction of SD parameter allows the tuning of the differential evolution from a completely asynchronous behavior to a super-synchronous behavior. Experiments show that a low SD generally improves the convergence speed and the convergence probability with respect to the classical synchronous DE. Moreover the ordering strategies introduced in ADE seem to improve the performances of the only already known asynchronous variant of DE (the Dynamical Differential Evolution Strategy).

An Extension of Algebraic Differential Evolution for the Linear Ordering Problem with Cumulative Costs

In this paper we propose an extension to the algebraic differential evolution approach for permutation based problems (DEP). Conversely from classical differential evolution, DEP is fully combinatorial and it is extended in two directions: new generating sets based on exchange and insertion moves are considered, and the case \(F>1\) is now allowed for the differential mutation operator. Moreover, also the crossover and selection operators of the original DEP have been modified in order to address the linear ordering problem with cumulative costs (LOPCC). The new DEP schemes are compared with the state-of-the-art LOPCC algorithms using a widely adopted benchmark suite. The experimental results show that DEP reaches competitive performances and, most remarkably, found 21 new best known solutions on the 50 largest LOPCC instances.

Algebraic Particle Swarm Optimization for the permutations search space

Particle Swarm Optimization (PSO), though being originally introduced for continuous search spaces, has been increasingly applied to combinatorial optimization problems. In particular, we focus on the PSO applications to permutation problems. As far as we know, the most popular PSO variants that produce permutation solutions are those based on random key techniques. In this paper, after highlighting the main criticalities of the random key approach, we introduce a totally discrete PSO variant for permutation-based optimization problems. The proposed algorithm, namely Algebraic PSO (APSO), simulates the original PSO design in permutations search space. APSO directly represents the particle positions and velocities as permutations. The APSO search scheme is based on a general algebraic framework for combinatorial optimization previously, and successfully, introduced in the context of discrete differential evolution schemes. The particularities of the PSO design scheme arouse new challenges for the algebraic framework: the non-commutativity of the velocity terms, and the rationale behind the PSO inertial move. Design solutions have been proposed for both the issues, and two APSO variants are provided. Experiments have been held to compare the performances of the APSO schemes with respect to the random key based PSO schemes in literature. Widely adopted benchmark instances of four popular permutation problems have been considered. The experimental results clearly show, with high statistical evidence, that APSO outperforms its competitors.

Optimal Design of Web Information Contents for E-Commerce Applications

Optimization of web content presentation poses a key challenge for e-commerce applications. Whether considering web pages, advertising banners or any other content presentation media on the web, the choice of the appropriate structure and appearance with respect to the given audience can obtain a more effective and successful impact on users, such as gathering more readers to web sites or customers to online shops. Here, the collective optimization of web content presentation based on the online discrete Particle Swarm Optimization (PSO) model is presented. The idea behind online PSO is to evaluate the collective user feedback as the PSO objective function which drives particles’ velocities in the hybrid continuous-discrete space of web content features. The PSO coordinates the process of sampling collective user behaviour in order to optimize a given user-based metric. Experiments in the online banner optimization scenario show that the method converges faster than other methods and avoid some common drawbacks such as local optima and hybrid discrete/continuous features management. The proposed online optimization method is sufficiently general and may be applied to other web marketing or business intelligence contexts.