Jorge Puente

A knowledge-based evolutionary strategy for scheduling problems with bottlenecks

Abstract In this paper we confront a family of scheduling problems by means of genetic algorithms: the job shop scheduling problem with bottlenecks. Our main contribution is a strategy to introduce specific knowledge into the initial population. This strategy exploits a probabilistic-based heuristic method that was designed to guide a conventional backtracking search. We report experimental results on two benchmarks, the first one includes a set of small problems and is taken from the literature. The second includes medium and large size problems and is proposed by our own. The experimental results show that the performance of the genetic algorithm clearly augments when the initial population is seeded with heuristic chromosomes, the improvement being more and more appreciable as long as the size of the problem instance increases. Moreover premature convergence which sometimes appears when randomness is limited in any way in a genetic algorithm is not observed.

Semantics of Schedules for the Fuzzy Job-Shop Problem

In the sequel, we consider the fuzzy job-shop problem, which is a variation of the job-shop problem where duration of tasks may be uncertain and where due-date constraints are allowed to be flexible. Uncertain durations are modeled using triangular fuzzy numbers, and due-date constraints are fuzzy sets with decreasing membership functions expressing a flexible threshold ldquoless than.rdquo Also, the objective function is built using fuzzy decision-making theory. We propose the use of a genetic algorithm (GA) to find solutions to this problem. Our aim is to provide a semantics for this type of problems and use this semantics in a methodology to analyze, evaluate, and, therefore, compare solutions. Finally, we present the results obtained using the GA and evaluate them using the proposed methodology.

Genetic tabu search for the fuzzy flexible job shop problem

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances.

A Memetic Approach to Fuzzy Job Shop Based on Expectation Model

In the sequel we consider a job shop problem with uncertain processing times modelled using triangular fuzzy numbers. A scheduling model based on the expected value of the makespan is introduced. Later, a genetic algorithm based on codification of permutations with repetitions, a decoding algorithm to generate possibly active schedules and a local search schema are defined in order to solve the job shop problem. Experimental results illustrate the potential of the proposed methods.

Coevolutionary makespan optimisation through different ranking methods for the fuzzy flexible job shop

In this paper we tackle a variant of the flexible job shop scheduling problem with uncertain task durations modelled as fuzzy numbers, the fuzzy flexible job shop scheduling problem or FfJSP in short. To minimise the schedules fuzzy makespan, we consider different ranking methods for fuzzy numbers. We then propose a cooperative coevolutionary algorithm with two different populations evolving the two components of a solution: machine assignment and task relative order. Additionally, we incorporate a specific local search method for each population. The resulting hybrid algorithm is then evaluated on existing benchmark instances, comparing favourably with the state-of-the-art methods. The experimental results also serve to analyse the influence in the robustness of the resulting schedules of the chosen ranking method.

Electric vehicle charging under power and balance constraints as dynamic scheduling

Display Omitted Electric vehicle charging scheduling is a Dynamic Constraint Satisfaction Problem.Imbalance constraints in a three phase electric feeder are considered.A new single machine scheduling problem with variable machine capacity is identified.The proposed scheduling model is evaluated by simulation on different scenarios. Scheduling appropriately the charging times for a set of electric vehicles may lead to energy savings but at the same time it may be a hard problem. In this paper, we consider a problem of this family, which is motivated by a private community park where each parking space belongs to a particular user and has a charging point connected to one line of a three-phase electric feeder. The number of vehicles in each line and the difference in the vehicles in every pair of lines charging at the same time are limited. We model this problem in the framework of Dynamic Constraint Satisfaction Problems (DCSP) with optimization, and so it is defined by a sequence of CSPs over time. We propose a solution method that decomposes each CSP into three instances of a one machine sequencing problem with variable capacity. This method was evaluated by simulation on a set of instances defined from different scenarios of vehicle arrivals, departures and energy requirements. The results of the experimental study show clearly that the proposed algorithm is efficient and that it outperforms a classic dispatching rule.

A genetic algorithm for robust berth allocation and quay crane assignment

Scheduling problems usually obtain the optimal solutions assuming that the environment is deterministic. However, actually the environment is dynamic and uncertain. Thus, the initial data could change and the initial schedule obtained might be unfeasible. To overcome this issue, a proactive approach is presented for scheduling problems without any previous knowledge about the incidences that can occur. In this paper, we consider the berth allocation problem and the quay crane assignment problem as a representative example of scheduling problems where a typical objective is to minimize the service time. The robustness is introduced within this problem by means of buffer times that should be maximized to absorb possible incidences or breakdowns. Therefore, this problem becomes a multi-objective optimization problem with two opposite objectives: minimizing the total service time and maximizing the robustness or buffer times.

Straight Line Programs: A New Linear Genetic Programming Approach

Tree encodings of programs are well known for their representative power and are used very often in Genetic Programming. In this paper we experiment with a new data structure, named straight line program (slp), to represent computer programs. The main features of this structure are described and new recombination operators for GP related to slps are introduced. Experiments have been performed on symbolic regression problems. Results are encouraging and suggest that the GP approach based on slps consistently outperforms conventional GP based on tree structured representations.

Heuristic local search for fuzzy open shop scheduling

We consider the fuzzy open shop scheduling problem, where task durations are assumed to be ill-known and modelled as triangular fuzzy numbers. We propose a neighbourhood structure for local search procedures, based on reversing critical arcs in the associated disjunctive graph. We provide a thorough theoretical study of the structure and, in particular, prove that feasibility and asymptotic convergence hold. We further illustrate its good behaviour with experimental results obtained by incorporating the local search procedure to an existing genetic algorithm from the literature and provide a new benchmark of problem instances.

Schedule generation schemes for job shop problems with fuzziness

We consider the job shop scheduling problem with fuzzy durations and expected makespan minimisation. We formally define the space of semi-active and active fuzzy schedules and propose and analyse different schedule-generation schemes (SGSs) in this fuzzy framework. In particular, we study dominance properties of the set of schedules obtained with each SGS. Finally, a computational study illustrates the great difference between the spaces of active and the semi-active fuzzy schedules, an analogous behaviour to that of the deterministic job shop.