Parameter estimation of a pressure swing adsorption model for air separation using multi-objective optimisation and support vector regression model

Simultaneous optimization of two or more objectives is an instance of multi-objective optimization (MOO). However, for most of the Multi-Objective Problems (MOPs), no single solution can optimize all the objective functions simultaneously. Evolutionary algorithms are a type of optimization algorithm used for constructing a well-distributed optimal front more quickly than a much more efficient approach. One of the most commonly used algorithms in this regard is differential evolution (DE). To solve the problem of non-dominated sorting for Multi-Objective DE (MODE), an approach is proposed that reduces the time complexity. DE is commonly recognized as one of the best methods for solving the MOPs. Several versions of DEs have been proposed for MOPs. This article proposes a novel mutation technique, named Environmental Parameter-based Multi-Objective Differential Evolution (EP-MODE) that acquires two additional environmental parameters to preserve diversity and accelerate the convergence. The proposed approach also reduces the time complexity of non-dominated sorting for Multi-Objective DE (MODE). The proposed mutation's performance has been evaluated on DTLZ series and ZDT series benchmark test functions on the Pareto-optimal front and compared with existing multi-objective algorithms (MODE and MODE-RMO). The solution comparatively verifies that the proposed EP-MODE outperforms most of the MODEs for lower dimension functions and higher functions. HIGHLIGHTS New environmental parameters-based mutation has been introduced in a differential evolution algorithm to solve multi-objective optimization problems (EP-mode) The addition of two additional environmental parameters to EP-mode has been found to be appropriate for maintaining diversity while also accelerating the convergence rate EP-MODE evaluated on bi-objective (DTLZ series) and tri-objective (ZDT series) benchmark test functions on the Pareto-optimal front and found EP-MODE's efficiency is higher than that of the MODE algorithm and the MODE algorithm with a ranking-based mutation operator GRAPHICAL ABSTRACT

Sensitivity analysis and automatic calibration of a rainfall–runoff model using multi-objectives

The structural design of Surface Acoustic Wave (SAW) filters is formulated as a constrained multi-objective optimization problem. Then three Evolutionary Multi-criterion Optimization (EMO) algorithms based on Differential Evolution (DE), namely, Multi-Objective DE (MODE), Non-dominated Sorting DE (NSDE), and Generalized DE 3 (GDE3), are applied to the three- and two-objective optimization problems of a balanced SAW filter. In order to compare the performances of the above EMO algorithms, several criteria including hypervolume are evaluated. As a result, it is shown that the performance of the EMO algorithm depends on the number of objective functions. Besides, in order to clarify the tradeoff relationship among the objective functions of the three-objective optimization problem, Principal Component Analysis (PCA) is employed.

Clinoptilolite: Untapped potential for kinetics gas separations

SUMMARYA general new methodology using evolutionary algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Differential Evolution (MODE), for obtaining optimal trajectory planning of an industrial robot manipulator (PUMA 560 robot) in the presence of fixed and moving obstacles with payload constraint is presented. The problem has a multi-criterion character in which six objective functions, 32 constraints and 288 variables are considered. A cubic NURBS curve is used to define the trajectory. The average fuzzy membership function method is used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find computational effort of the NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed. Both NSGA-II and MODE are best for this problem.

Particle swarm optimization (PSO) and differential evolution (DE) are meta-heuristics which have been found to be successful in a wide variety of optimization tasks. The high speed of convergence and the relative simplicity of PSO make it a highly viable candidate to be used in multi-objective optimization problems (MOPs). Therefore, several PSO approaches capable to handle MOPs (MOPSOs) have appeared in the past. There are some problems, however, where PSO-based algorithms have shown a premature convergence. On the other hand, multi- objective DEs (MODE) have shown lower speed of convergence than MOPSOs but they have been successfully used in problems where MOPSO have mistakenly converged. In this work, we have developed experiments to observe the convergence behavior, the online convergence, and the diversity of solutions of both meta-heuristics in order to have a better understanding about how particles and solutions move in the search space. To this end, MOPSO and MODE algorithms under (to our best effort) similar conditions were used. Moreover, the ZDT test suite was used on all experiments since it allows to observe Pareto fronts in two-dimensional scatter plots (more details on this are presented on the experiments section). Based on the observations found, modifications to two PSO-based algorithms from the state of the art were proposed resulting in a rise on their performance. It is concluded that MOPSO presents a poor distributed scheme that leads to a more aggressive search. This aggressiveness showed to be detrimental for the selected problems. On the other hand, MODE seemed to generate better distributed points on both decision and objective space allowing it to produce better results.

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

Naphtha pyrolysis is one of the important routes for simultaneous production of ethylene and propylene. With recent increase in demand of both ethylene and propylene, understanding of naphtha pyrolysis becomes important for producing with increasing yield of these valuable products. Simultaneous maximization of yield of these two products is mathematically formulated as a multiobjective optimization (MOO) problem. Improved selected scheme is incorporated in the existing multiobjective differential evolution (MODE) algorithm and a new evolutionary algorithm is proposed. Both the evolutionary algorithms [i.e., MODE III and MODE-III with improved selection scheme (MODE III-ISS)] are used for MOO of industrial naphtha cracker unit. Two objectives (maximization of ethylene yield and propylene yield) and decision variables [pressure of the reactor tube (P), temperature of the reactor (T), initial flow rate of naphtha (F 0), and steam to naphtha ratio (SOR)] are considered for MOO study. MODE III and MODE III-ISS algorithms results are compared and presented, which clearly shows that the proposed MODE III-ISS algorithm possesses certain advantages over the MODE III algorithm (such as number of successful selections and percentage convergence with respect to initial number of population points, the quality of the obtained nondominated [ND] solutions).

Profit optimization for bio-gas upgrading PSA process based on controlling step-time

MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules

Urban water distribution networks are crucial infrastructures for providing essential services to society, but their exorbitant costs and limited water resources make their optimization a critical research area. Optimal management and design of these networks can help to reduce costs and enhance their efficiency while meeting technical, economic, and quality standards. In particular, the management of network pressure is critical for reducing leakage in water distribution systems. Thus, this study aimed to investigate two objective functions for optimizing the water distribution network: (i) minimizing costs while considering the number of pressure-relief valves, and (ii) minimizing network pressure by observing the optimal pressure range. To achieve this, the Nondominated Sorting Differential Evolution (NSDE) multi-objective metaheuristic algorithm was employed as the optimization tool, and a computer program was written in MATLAB software for solving the optimization models. EPANET software was also used for hydraulic simulation of the water distribution network. The efficiency and capabilities of these models were tested on the case study of the third district of Mashhad in Iran. The results indicated that the installation and adjustment of pressure-relief valves in accordance with the positions and optimal settings of the output of the proposed models significantly improved the desired goals, particularly the average pressure of the network. As an example of optimization, the study achieved a 56.12% reduction in pressure compared to the case without a plan, considering five pressure-relief valves.

This paper presents an application of the Multiobjective Differential Evolution (MoDE) algorithm for the optimal operation of a complex multipurpose reservoir system. The developed algorithm (MoDE) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the case study. The case study includes part of a complex water supply system located in southwest Brazil that provides water for approximately 20 million people in the Sao Paulo metropolitan area (SPMA). The objectives of the case study include minimization of demand shortage (the difference between demand for water and available water supply), maximization of water quality (or minimization of the deviation from the water quality standards), and minimization of pumping cost. MoDE is applied to the case study using two inflow scenarios: (1) a drought period with inflows below historical average; and (2) a wet period with inflows above historical average. Multiobjective analysis is done by comparing two pairs of objective functions: minimization of demand shortage versus minimization of pumping cost and minimization of demand shortage versus minimization of the deviation from water quality standards. The constraints for the analysis are reservoir capacity, tunnels and channel limitations, and minimum downstream flow for all reservoirs. The proposed MoDE algorithm is outperforming NSGA-II as it converges closer to and provides better spread coverage of the true Pareto front.

Memetic Elitist Pareto Differential Evolution algorithm based Radial Basis Function Networks for classification problems

Optimization problems are ubiquitous and consequential. In fact every sphere of human activity that can be quantified can be formulated as an optimization problem. The focus of my work is on Global Optimization which is not only desirable but also necessary in many cases. In the past few decades several Global optimization algorithms have been suggested in literature out of which stochastic, population based search algorithms like Genetic algorithms (GA), Evolutionary Strategies (ES), Swarm Algorithms (Ant Colony (ACO) and Particle Swarm (PSO)), differential Evolution etc. have become immensely popular for solving real life optimization problems. The reason, being the efficiency with which these algorithms can tackle the complex and intricate models of real life problems. My research is concentrated on Differential Evolution which is relatively a newer addition to the population based search algorithms. DE was first suggested by Storn and Price in 1995 as a search technique for solving optimization problems. It uses the same operators like mutation, crossover and selection as that of GA but manipulates them in a manner different to that of GA.

The multiobjective differential evolution (MODE), which is an extension of the Differential Evolution (DE), is applied to solve the multiobjective optimization problem (MOOP) of wet film Poly-Ethylene Terephthalate (PET) reactor considering minimization of acid end group and vinyl end group as the main objectives. The objective function is modified to solve five different possible cases. The results show that a Pareto set (a set of equally good solutions) is obtained for the cases when two of the parameters (residence time of the polymeric reaction mass, θ, and the speed of the wiped-film agitator, N) are considered as decision variables, unlike a unique solution obtained using Nondominated Sorting Genetic Algorithm (NSGA). The Pareto optimal front provides wide-ranging optimal sets of operating conditions. And an appropriate set of operating conditions can be selected based on the requirements of the user.