SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing

Performance evaluation on optimisation of 200 dimensional numerical tests - results and issues

Abstract: Many tasks in science and technology require optimisation. Resolving such tasks could bring great benefits to community. Multidimensional problems where optimisation parameters are hundreds and more face unusual computational limitations. Algorithms, which perform well on low number of dimensions, when are applied to high dimensional space suffers insuperable difficulties. This article presents an investigation on 200 dimensional scalable, heterogeneous, real-value, numerical tests. For some of these tests optimal values are dependent on dimensions’ number and virtually unknown for variety of dimensions. Dependence on initialisation for successful identification of optimal values is analysed by comparison between experiments with start from random initial locations and start from one location. The aim is to: (1) assess dependence on initialisation in optimisation of 200 dimensional tests; (2) evaluate tests complexity and required for their resolving periods of time; (3) analyse adaptation to tasks with unknown solutions; (4) identify specific peculiarities which could support the performance on high dimensions (5) identify computational limitations which numerical methods could face on high dimensions. Presented and analysed experimental results can be used for further comparison and evaluation of real value methods

Performance evaluation on optimisation of 200 dimensional numerical tests - results and issues

Abstract: Many tasks in science and technology require optimisation. Resolving such tasks could bring great benefits to community. Multidimensional problems where optimisation parameters are hundreds and more face unusual computational limitations. Algorithms, which perform well on low number of dimensions, when are applied to high dimensional space suffers insuperable difficulties. This article presents an investigation on 200 dimensional scalable, heterogeneous, real-value, numerical tests. For some of these tests optimal values are dependent on dimensions’ number and virtually unknown for variety of dimensions. Dependence on initialisation for successful identification of optimal values is analysed by comparison between experiments with start from random initial locations and start from one location. The aim is to: (1) assess dependence on initialisation in optimisation of 200 dimensional tests; (2) evaluate tests complexity and required for their resolving periods of time; (3) analyse adaptation to tasks with unknown solutions; (4) identify specific peculiarities which could support the performance on high dimensions (5) identify computational limitations which numerical methods could face on high dimensions. Presented and analysed experimental results can be used for further comparison and evaluation of real value methods

Economic and environmental strategies for process design

This paper first addresses the definition of various objectives involved in eco-efficient processes, taking simultaneously into account ecological and economic considerations. The environmental aspect at the preliminary design phase of chemical processes is quantified by using a set of metrics or indicators following the guidelines of sustainability concepts proposed by . The resulting multiobjective problem is solved by a genetic algorithm following an improved variant of the so-called NSGA II algorithm. A key point for evaluating environmental burdens is the use of the package ARIANE™, a decision support tool dedicated to the management of plants utilities (steam, electricity, hot water, etc.) and pollutants (CO2, SO2, NO, etc.), implemented here both to compute the primary energy requirements of the process and to quantify its pollutant emissions. The well-known benchmark process for hydrodealkylation (HDA) of toluene to produce benzene, revisited here in a multiobjective optimization way, is used to illustrate the approach for finding eco-friendly and cost-effective designs. Preliminary biobjective studies are carried out for eliminating redundant environmental objectives. The trade-off between economic and environmental objectives is illustrated through Pareto curves. In order to aid decision making among the various alternatives that can be generated after this step, a synthetic evaluation method, based on the so-called Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) (), has been first used. Another simple procedure named FUCA has also been implemented and shown its efficiency vs. TOPSIS. Two scenarios are studied; in the former, the goal is to find the best trade-off between economic and ecological aspects while the latter case aims at defining the best compromise between economic and more strict environmental impact