The Pareto curve in an exact way for multi-objective differentiable functions with constraints

2021 ◽  
Vol 42 (8) ◽  
pp. 1907-1922
Author(s):  
El Kadi Hellel ◽  
Samir Hamaci ◽  
Rezki Ziani
Keyword(s):  
Multi Objective ◽  
Pareto Curve ◽  
Differentiable Functions

Kinematic Multi-Objective Optimization of Circular-Toothed Gerotor Pumps by Genetic Algorithm

2017 ◽  
Author(s):  
Andrew J. Robison ◽  
Andrea Vacca
Keyword(s):  
Genetic Algorithm ◽  
Design Method ◽  
Third Party ◽  
Low Flow ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Generation Algorithm ◽  
Multi Objective ◽  
Pareto Curve

A gerotor gear generation algorithm has been developed that evaluates key performance objective functions to be minimized or maximized, and then an optimization algorithm is applied to determine the best design. Because of their popularity, circular-toothed gerotors are the focus of this study, and future work can extend this procedure to other gear forms. Parametric equations defining the circular-toothed gear set have been derived and implemented. Two objective functions were used in this kinematic optimization: maximize the ratio of displacement to pump radius, which is a measure of compactness, and minimize the kinematic flow ripple, which can have a negative effect on system dynamics and could be a major source of noise. Designs were constrained to ensure drivability, so the need for additional synchronization gearing is eliminated. The NSGA-II genetic algorithm was then applied to the gear generation algorithm in modeFRONTIER, a commercial software that integrates multi-objective optimization with third-party engineering software. A clear Pareto front was identified, and a multi-criteria decision-making genetic algorithm was used to select three optimal designs with varying priorities of compactness vs low flow variation. In addition, three pumps used in industry were scaled and evaluated with the gear generation algorithm for comparison. The scaled industry pumps were all close to the Pareto curve, but the optimized designs offer a slight kinematic advantage, which demonstrates the usefulness of the proposed gerotor design method.

scholarly journals Multi-objective optimization of the management of a waterworks using an integrated well field model

2012 ◽  
Vol 43 (4) ◽  
pp. 430-444 ◽  
Author(s):  
Annette K. Hansen ◽  
Henrik Madsen ◽  
Peter Bauer-Gottwein ◽  
Anne Katrine V. Falk ◽  
Dan Rosbjerg
Keyword(s):  
Energy Consumption ◽  
Field Model ◽  
Contaminated Site ◽  
Test Case ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Curve ◽  
Well Field ◽  
Production Wells ◽  
The Individual

This study uses multi-objective optimization of an integrated well field model to improve the management of a waterworks. The well field model, called WELLNES (WELL field Numerical Engine Shell) is a dynamic coupling of a groundwater model, a pipe network model, and a well model. WELLNES is capable of predicting the water level and the energy consumption of the individual production wells. The model has been applied to Søndersø waterworks in Denmark, where it predicts the energy consumption within 1.8% of the observed. The objectives of the optimization problem are to minimize the specific energy of the waterworks and to avoid inflow of contaminated water from a nearby contaminated site. The decision variables are the pump status (on/off), and the constraint is that the waterworks has to provide a certain amount of drinking water. The advantage of multi-objective optimization is that the Pareto curve provides the decision-makers with compromise solutions between the two competing objectives. In the test case the Pareto optimal solutions are compared with an exhaustive benchmark solution. It is shown that the energy consumption can be reduced by 4% by changing the pumping configuration without violating the protection against contamination.

A Novel Multiobjective Optimization for Cement Stabilized Soft Soil based on Artificial Bee Colony

2020 ◽  
pp. 285-303
Author(s):  
Rahul Khandelwal ◽  
J. Senthilnath ◽  
S. N. Omkar ◽  
Narendra Shivanath
Keyword(s):  
Artificial Bee Colony ◽  
Soil Stabilization ◽  
Cement Content ◽  
Soft Soil ◽  
Target Strength ◽  
Curing Time ◽  
Multi Objective ◽  
Pareto Curve ◽  
Bee Colony ◽  
Multiple Swarms

Cement is the most widely used additive in soft soil stabilization due to its high strength and availability. The cement content and curing time have a direct influence on the stabilization cost and hence it is prudent to minimize these variables to achieve optimality. Thus, it is a classical multi-objective optimization problem to find the optimum combination of cement content used and the curing time provided to achieve the target strength. This paper brings out the use of Vector Evaluated Artificial Bee Colony (VEABC) algorithm, a multi-objective variant of Artificial Bee Colony (ABC) technique, for the problem on hand. VEABC is a swarm intelligence algorithm, which employs multiple swarms to handle the multiple objectives and the information migration between these swarms ensures a global optimum solution is reached. Due to the stochastic nature of ABC algorithm, the resulting Pareto Curve will cover a good range of data with smooth transition. The Pareto fronts obtained for target strength could be used as calibration charts for scheduling the soft soil stabilization activities.

Engineering System Design Using Firefly Algorithm and Multi-Objective Optimization

2011 ◽  
Author(s):  
Fran Se´rgio Lobato ◽  
Edu Barbosa Arruda ◽  
Aldemir Ap. Cavalini ◽  
Valder Steffen
Keyword(s):  
Firefly Algorithm ◽  
Optimization Problems ◽  
Evolutionary Strategies ◽  
Engineering System ◽  
Multi Objective Optimization ◽  
Present Contribution ◽  
Multi Objective ◽  
Pareto Curve ◽  
Rotary Dryer ◽  
Engineering System Design

Modern engineering problems, such as aircraft or automobile design, are often composed by a large number of variables that must be chosen simultaneously for better design performance. Normally, most of these parameters are conflicting, i.e., an improvement in one of them does not lead, necessarily, to better results for the other ones. Thus, many methods to solve multi-objective optimization problems (MOP) have been proposed. The MOP solution, unlike the single objective problems, is a set of non-dominated solutions that form the Pareto Curve, also known as Pareto Optimal. Among the MOP algorithms, we can cite the Firefly Algorithm (FA). FA is a bio-inspired method that mimics the patterns of short and rhythmic flashes emitted by fireflies in order to attract other individuals to their vicinities. For illustration purposes, in the present contribution the FA, associated with the Pareto dominance criterion, is applied to three different design cases. The first one is related to the geometric design of a clamped-free beam. The second one deals with the project of a welded beam and the last one focuses on estimating the characteristic parameters of a rotary dryer pilot plant. The proposed methodology is compared with other evolutionary strategies. The results indicate that the proposed approach characterizes an interesting alternative for multi-objective optimization problems.

Towards a global multi objective optimization of wastewater treatment plant based on modeling and genetic algorithms

2007 ◽  
Vol 56 (9) ◽  
pp. 109-116 ◽  
Author(s):  
B. Béraud ◽  
J.P. Steyer ◽  
C. Lemoine ◽  
E. Latrille ◽  
G. Manic ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Waste Water Treatment ◽  
Treatment Plant ◽  
Water Treatment Plant ◽  
Waste Water Treatment Plant ◽  
Multi Objective ◽  
Pareto Curve ◽  
Multi Objective Genetic Algorithm ◽  
Trade Offs ◽  
Pi Controllers

The optimization of the Benchmark Simulation Model 1 (BSM1) through a multi objective genetic algorithm (MOGA) is studied in this paper. First, the optimization of the set points of the two Proportional Integral (PI) controllers proposed in BSM1 is performed. Then, a new controller layout composed of three PI controllers is proposed and the set points are also optimized. Among all performance indexes proposed in BSM1, only the effluent quality and the energy consumption for pumping and aeration were taken into account in both optimization problems. Since these two objectives are conflicting, the use of the MOGA allows in both cases a direct visualization of the possible trade-offs through a Pareto curve. These two case studies showed the feasibility of such optimizations even when dealing with computing intensive model like the full scale waste water treatment plant (WWTP) model.

scholarly journals An oppositional Salp Swarm: Jaya algorithm for thermal design optimization of an Organic Rankine Cycle

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Mert Sinan Turgut ◽  
Oguz Emrah Turgut
Keyword(s):  
Optimization Problems ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Thermal Design ◽  
Design Parameters ◽  
Nsga Ii ◽  
Multi Objective ◽  
Specific Investment ◽  
Weighted Sum Method ◽  
Pareto Curve

AbstractThis study proposes a hybrid metaheuristic algorithm to tackle both single and multi objective optimization problems that are subjected to hard constraints. Twenty-four single objective optimization benchmark problems comprising unimodal and multi modal test functions have been solved by the proposed hybrid algorithm (OPSSAJ) and numerical results have been compared with those acquired by some of the new emerged metaheuristic optimizers. The proposed OPSSAJ shows a significant accuracy and robustness in most of the cases and proves its efficiency in solving high dimensional problems. As a real-world case study, seventeen operational design parameters of an organic rankine cycle (ORC) operating with a binary mixture of R227EA and R600 refrigerants are optimized by the proposed hybrid OPSSAJ to obtain the optimum values of contradicting dual objectives of second law efficiency and Specific Investment Cost. A Pareto curve composed of non-dominated solutions is constructed through the weighted sum method and the final solution is chosen by the reputed TOPSIS decision-maker. The pareto curve and best-compromising result obtained by utilizing the OPPSAJ are compared with that of acquired by using nondominated sorting genetic algorithm II (NSGA-II) and multiple objective particle swarm optimization (MOPSO) algorithms. The multi-objective ORC design obtained with the OPSSAJ yields a significant improvement in thermal efficiency and cost values compared to designs found by the NSGA-II and MOPSO algorithms. Furthermore, a sensitivity analysis is performed to observe the influences of the selected design variables on problem objectives.

Fuzzy multi-objective decision making approach for nuclear power plant installation

2020 ◽  
Vol 39 (5) ◽  
pp. 6339-6350
Author(s):  
Esra Çakır ◽  
Ziya Ulukan
Keyword(s):  
Linear Programming ◽  
Power Plant ◽  
Nuclear Power Plant ◽  
Energy Supply ◽  
Energy Demand ◽  
Nuclear Power ◽  
Power Plants ◽  
Total Duration ◽  
Objective Functions ◽  
Multi Objective

Due to the increase in energy demand, many countries suffer from energy poverty because of insufficient and expensive energy supply. Plans to use alternative power like nuclear power for electricity generation are being revived among developing countries. Decisions for installation of power plants need to be based on careful assessment of future energy supply and demand, economic and financial implications and requirements for technology transfer. Since the problem involves many vague parameters, a fuzzy model should be an appropriate approach for dealing with this problem. This study develops a Fuzzy Multi-Objective Linear Programming (FMOLP) model for solving the nuclear power plant installation problem in fuzzy environment. FMOLP approach is recommended for cases where the objective functions are imprecise and can only be stated within a certain threshold level. The proposed model attempts to minimize total duration time, total cost and maximize the total crash time of the installation project. By using FMOLP, the weighted additive technique can also be applied in order to transform the model into Fuzzy Multiple Weighted-Objective Linear Programming (FMWOLP) to control the objective values such that all decision makers target on each criterion can be met. The optimum solution with the achievement level for both of the models (FMOLP and FMWOLP) are compared with each other. FMWOLP results in better performance as the overall degree of satisfaction depends on the weight given to the objective functions. A numerical example demonstrates the feasibility of applying the proposed models to nuclear power plant installation problem.

Fuzzy multi-objective location and routing problem

2020 ◽  
Vol 39 (3) ◽  
pp. 3259-3273
Author(s):  
Nasser Shahsavari-Pour ◽  
Najmeh Bahram-Pour ◽  
Mojde Kazemi
Keyword(s):  
Firefly Algorithm ◽  
High Reliability ◽  
Research Area ◽  
Nsga Ii ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Location Allocation ◽  
Multi Objective ◽  
Location Routing ◽  
The Cost

The location-routing problem is a research area that simultaneously solves location-allocation and vehicle routing issues. It is critical to delivering emergency goods to customers with high reliability. In this paper, reliability in location and routing problems was considered as the probability of failure in depots, vehicles, and routs. The problem has two objectives, minimizing the cost and maximizing the reliability, the latter expressed by minimizing the expected cost of failure. First, a mathematical model of the problem was presented and due to its NP-hard nature, it was solved by a meta-heuristic approach using a NSGA-II algorithm and a discrete multi-objective firefly algorithm. The efficiency of these algorithms was studied through a complete set of examples and it was found that the multi-objective discrete firefly algorithm has a better Diversification Metric (DM) index; the Mean Ideal Distance (MID) and Spacing Metric (SM) indexes are only suitable for small to medium problems, losing their effectiveness for big problems.

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