Strategies for multiobjective genetic algorithm development: Application to optimal batch plant design in process systems engineering

This work deals with multiobjective optimization problems using Genetic Algorithms (GA). A MultiObjective GA (MOGA) is proposed to solve multiobjective problems combining both continuous and discrete variables. This kind of problem is commonly found in chemical engineering since process design and operability involve structural and decisional choices as well as the determination of operating conditions. In this paper, a design of a basic MOGA which copes successfully with a range of typical chemical engineering optimization problems is considered and the key points of its architecture described in detail. Several performance tests are presented, based on the influence of bit ranging encoding in a chromosome. Four mathematical functions were used as a test bench. The MOGA was able to find the optimal solution for each objective function, as well as an important number of Pareto optimal solutions. Then, the results of two multiobjective case studies in batch plant design and retrofit were presented, showing the flexibility and adaptability of the MOGA to deal with various engineering problems

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods

Automatic methods for model calibration seek to take advantage of the speed and power of digital computers, while being objective and relatively easy to implement. However, they do not provide parameter estimates and hydrograph simulations that are considered acceptable by the hydrologists responsible for operational forecasting and have therefore not entered into widespread use. In contrast, the manual approach which has been developed and refined over the years to result in excellent model calibrations is complicated and highly labor-intensive, and the expertise acquired by one individual with a specific model is not easily transferred to another person (or model). In this paper, we propose a hybrid approach that combines the strengths of each. A multicriteria formulation is used to "model" the evaluation techniques and strategies used in manual calibration, and the resulting optimization problem is solved by means of a computerized algorithm. The new approach provides a stronger test of model performance than methods that use a single overall statistic to aggregate model errors over a large range of hydrologic behaviors. The power of the new approach is illustrated by means of a case study using the Sacramento Soil Moisture Accounting model

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Identification of quasi-optimal regions in the design space using surrogate modeling

The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to find optimal performance characteristics of expensive simulations (forward analysis: from input to optimal output). However, often the practitioner knows a priori the desired performance and is interested in finding the associated input parameters (reverse analysis: from desired output to input). A popular method to solve such reverse (inverse) problems is to minimize the error between the simulated performance and the desired goal. However, there might be multiple quasi-optimal solutions to the problem. In this paper, the authors propose a novel method to efficiently solve inverse problems and to sample Quasi-Optimal Regions (QORs) in the input (design) space more densely. The development of this technique, based on the probability of improvement criterion and kriging models, is driven by a real-life problem from bio-mechanics, i.e., determining the elasticity of the (rabbit) tympanic membrane, a membrane that converts acoustic sound wave into vibrations of the middle ear ossicular bones

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods