Claudio Fabiano Motta Toledo

A hybrid multi-population genetic algorithm applied to solve the multi-level capacitated lot sizing problem with backlogging

The present paper proposes a new hybrid multi-population genetic algorithm (HMPGA) as an approach to solve the multi-level capacitated lot sizing problem with backlogging. This method combines a multi-population based metaheuristic using fix-and-optimize heuristic and mathematical programming techniques. A total of four test sets from the MULTILSB (Multi-Item Lot-Sizing with Backlogging) library are solved and the results are compared with those reached by two other methods recently published. The results have shown that HMPGA had a better performance for most of the test sets solved, specially when longer computing time is given.

Um modelo de otimização para o problema integrado de dimensionamento de lotes e programação da produção em fábricas de refrigerantes

The present paper establishes, describes mathematically and solves a multi-level lot sizing and scheduling problem in an industrial set with parallel machines and sequence-dependent setup cost and time. The problem is motivated by real situations found in some industrial settings mainly the soft drink industry. In this kind of industry, the production involves two interdependent levels with decisions about raw material storage and soft drink bottling. The several raw materials are stored in tanks from which they flow to the bottling lines. The challenge is to determine simultaneously the minimum cost lot sizing and scheduling of raw material in tanks and also in the bottling lines, where setup costs and time depend on the previous items stored and bottled. A mixed-integer mathematical model with several combined constrains that use to be handled apart in the literature is proposed. The lack of similar models led us to create a set of instances to evaluate the model and the solution techniques developed. The instances were optimally solved by the GAMS/Cplex software. Due to the problem complexity, it is demonstrated that the use of this optimization package is only viable for small-sized instances. The computational results are showed and analyzed.

Global optimization using a genetic algorithm with hierarchically structured population

This paper applies a genetic algorithm with hierarchically structured population to solve unconstrained optimization problems. The population has individuals distributed in several overlapping clusters, each one with a leader and a variable number of support individuals. The hierarchy establishes that leaders must be fitter than its supporters with the topological organization of the clusters following a tree. Computational tests evaluate different population structures, population sizes and crossover operators for better algorithm performance. A set of known benchmark test problems is solved and the results found are compared with those obtained from other methods described in the literature, namely, two genetic algorithms, a simulated annealing, a differential evolution and a particle swarm optimization. The results indicate that the method employed is capable of achieving better performance than the previous approaches in regard as the two criteria usually employed for comparisons: the number of function evaluations and rate of success. The method also has a superior performance if the number of problems solved is taken into account.

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

This study applies a genetic algorithm embedded with mathematical programming techniques to solve a synchronized and integrated two-level lot sizing and scheduling problem motivated by a real-world problem that arises in soft drink production. The problem considers a production process compounded by raw material preparation/storage and soft drink bottling. The lot sizing and scheduling decisions should be made simultaneously for raw material preparation/storage in tanks and soft drink bottling in several production lines minimizing inventory, shortage and setup costs. The literature provides mixed-integer programming models for this problem, as well as solution methods based on evolutionary algorithms and relax-and-fix approaches. The method applied by this paper uses a new approach which combines a genetic algorithm (GA) with mathematical programming techniques. The GA deals with sequencing decisions for production lots, so that an exact method can solve a simplified linear programming model, responsible for lot sizing decisions. The computational results show that this evolutionary/mathematical programming approach outperforms the literature methods in terms of production costs and run times when applied to a set of real-world problem instances provided by a soft drink company.

An approach based on hybrid genetic algorithm applied to image denoising problem

Graphical abstractDisplay Omitted An approach based on hybrid genetic algorithm (HGA) is proposed for image denoising. In this problem, a digital image corrupted by a noise level must be recovered without losing important features such as edges, corners and texture. The HGA introduces a combination of genetic algorithm (GA) with image denoising methods. During the evolutionary process, this approach applies some state-of-the-art denoising methods and filtering techniques, respectively, as local search and mutation operators. A set of digital images, commonly used by the scientific community as benchmark, is contaminated by different levels of additive Gaussian noise. Another set composed of some Satellite Aperture Radar (SAR) images, corrupted with a multiplicative speckle noise, is also used during the tests. First, the computational tests evaluate several alternative designs from the proposed HGA. Next, our approach is compared against literature methods on the two mentioned sets of images. The HGA performance is competitive for the majority of the reported results, outperforming several state-of-the-art methods for images with high levels of noise.

A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems.

A Hybrid Multi-Population Genetic Algorithm for UAV Path Planning

This paper proposes a hybrid method to define a path planning for unmanned aerial vehicles in a non-convex environment with uncertainties. The environment becomes non-convex by the presence of no-fly zones such as mountains, cities and airports. Due to the uncertainties related to the path planning in real situations, risk of collision can not be avoided. Therefore, the planner must take into account a lower level of risk than one tolerated by the user. The proposed hybrid method combines a multi-population genetic algorithm with visibility graph. This is done by encoding all possible paths as individuals and solving a linear programming model to define the full path to be executed by the aircraft. The hybrid method is evaluated from a set of 50 maps and compared against an exact and heuristic approaches with promising results reported.

A Multi-population Genetic Algorithm for UAV Path Re-planning under Critical Situation

This paper studies the path planning for Unmanned Aerial Vehicles (UAVs) under critical situations, where the aircraft has to execute a hard landing. Such critical situations can be provoked by equipment failures or extreme environmental situations that demand the UAV to abort the mission running and to land the aircraft without risk for people, properties and itself. First, a mathematical formulation is introduced to describe this problem. A planner system is proposed based on a multi-population genetic algorithm and a greedy heuristic. Computational results are conducted over a large set of scenarios with different levels of difficulty. Also, some simulations are executed using FlightGear simulator to illustrate the UAVs behaviour when landing under different wind velocities. The results achieved indicate the greedy heuristic is able to define faster feasible landing paths, whose quality can be improved by the evolutionary approach always within a short computation time.

A multi-population genetic algorithm approach for PID controller auto-tuning

The present paper applies a multi-population genetic algorithm (MPGA) to the Proportional, Integral and Derivative (PID) controller tuning problem. Two control criteria were optimized, the integral of the time multiplied by the absolute error (ITAE), and the integral of the time multiplied by the absolute output (ITAY). The MPGA is compared with a standard genetic algorithms (SGA) already applied to the same control model. The control criteria are supplied by neural networks (NN) previously trained for this purpose. The control tuning and the corresponding responses were obtained using the MATLAB/SIMULNK environment. The computational results show a superior performance of the MPGA even when compared with the exact values found by dynamic simulation using gradient techniques.

A hybrid heuristic approach to solve the multi level capacitated lot sizing problem

This paper presents preliminary results found by a hybrid heuristic applied to solve the Multi-Level Capacitated Lot Sizing Problem (MLCLSP). The proposed method combines a multi-population genetic algorithm and fix-and-optimize heuristic. These methods are also integrated to a mathematical programming approach. For this, a mathematical reformulation of MLCLSP model is proposed to embed the exact solution of the model in the heuristic approaches. The hybrid heuristic is evaluated in two sets of benchmark instances. The solutions found are compared with those reached by other methods from literature. The preliminary results obtained indicate that the hybrid heuristic outperforms other approaches in the majority of problems solved.