Marco Baioletti

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.

Conditional independence structure and its closure: Inferential rules and algorithms

In this paper, we deal with conditional independence models closed with respect to graphoid properties. Such models come from different uncertainty measures, in particular in a probabilistic setting. We study some inferential rules and describe methods and algorithms to compute efficiently the closure of a set of conditional independence statements.

Inferential models and relevant algorithms in a possibilistic framework

We provide a general inferential procedure based on coherent conditional possibilities and we show, by some examples, its possible use in medical diagnosis. In particular, the role of the likelihood in possibilistic setting is discussed and once the coherence of prior possibility and likelihood is checked, we update prior possibilities.

Elimination of Boolean variables for probabilistic coherence

Abstract In this paper we deal with the computational complexity problem of checking the coherence of a partial probability assessment (called CPA). The CPA problem, like its analogous PSAT, is NP-complete so we look for an heuristic procedure to make tractable reasonable instances of the problem. Starting from the characteristic feature of de Finettis approach (i.e. the explicit distinction between the probabilistic assessment and the logical relations among the sentences) we introduce several rules for a sequential “elimination” of Boolean variables from the domain of the assessment. The procedure resembles the well-known Davis-Putnam rules for the satisfiability, however we have, as a drawback, the introduction of constraints (among real variables) whose satisfiability must be checked. In simple examples we test the efficiency of the procedure respect to the “traditional” approach of solving a linear system with a huge coefficient matrix built from the atoms generated by the domain of the assessment.

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.

Experimental evaluation of pheromone models in ACOPlan

In this paper the system ACOPlan for planning with non uniform action cost is introduced and analyzed. ACOPlan is a planner based on the ant colony optimization framework, in which a colony of planning ants searches for near optimal solution plans with respect to an overall plan cost metric. This approach is motivated by the strong similarity between the process used by artificial ants to build solutions and the methods used by state–based planners to search solution plans. Planning ants perform a stochastic and heuristic based search by interacting through a pheromone model. The proposed heuristic and pheromone models are presented and compared through systematic experiments on benchmark planning domains. Experiments are also provided to compare the quality of ACOPlan solution plans with respect to state of the art satisficing planners. The analysis of the results confirm the good performance of the Action–Action pheromone model and points out the promising performance of the novel Fuzzy–Level–Action pheromone model. The analysis also suggests general principles for designing performant pheromone models for planning and further extensions of ACOPlan to other optimization models.

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.

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.