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Exploring trade-offs among the multiple benefits of green-blue-grey infrastructure
Published in Alida Ivana Alves Beloqui, Combining Green-Blue-Grey Infrastructure for Flood Mitigation and Enhancement of Co-Benefits, 2020
Different parameters can be chosen when applying the NSGA-II algorithm, such as population size, number of generations, and mutation and crossover operators. Several runs of the framework were performed to assess convergence and to choose the values of these parameters. Three indicators were used for Pareto fronts evaluation: the number of non-dominated solutions obtained in the final Pareto compared to the given number of initial population, the extent or spread of Pareto fronts with respect to the objectives, and the average space among solutions. We analysed the sensitivity of optimisation results to the parameters. Since the theoretical value of mutation is the inverse of decision variables (Mala-Jetmarova et al., 2015), this analysis was applied for the cases of maximum and minimum number of variables. Changing values of population (between 80 and 400), generations (between 20 and 80), crossover (between 0.2 and 0.9) and mutation (between 0.01 and 0.08), the values of number of non-dominated solutions, extend of Pareto curve and average space among solutions were evaluated. As a result, values of 350 individuals for population, 70 generations, 0.9 for crossover and 0.021 for mutation were selected to apply the optimisation framework.
Carbon Policies for Reducing Emissions in Power Plants through an Optimization Framework
Published in Subhas K Sikdar, Frank Princiotta, Advances in Carbon Management Technologies, 2020
Aurora del Carmen Munguía-López, José María Ponce-Ortega
On the other hand, the results involving the carbon tax credits are shown in Figure 4. When the highest compensation values are evaluated (120 and 130 $/ton CO2), important reductions in emissions throughout the Pareto front are obtained. Therefore, a maximum profit solution including low emissions can be attained. Notice that with the rest of the tax credits, only variations in the profit are observed. The impact of considering the penalizations and compensations in the integrated system can be observed by comparing the results with the generated emissions in a conventional system (without CLC or algae systems). This comparison is presented in Figure 5. The three solutions can be compared because their optimal configuration for the technologies in the power plant is equal and, thus, the net electricity is as well. Note that the highest compensation and the lowest penalization were considered in order to find the best economic and environmental solution (as described above, no further reduction of the emissions was found with greater taxes). The reduction in emissions for the considered tax and tax credit scenarios is similar: 70 and 71%, respectively. Regarding the economic objective, higher profits are attained with the carbon compensations. Therefore, it is concluded that involving tax credits for the avoided emissions gives better tradeoffs among the objective functions. Furthermore, the benefits of considering carbon policies as a strategy to reduce emissions and simultaneously attain a profitable system of power generation and biofuels production are identified. Through the different tradeoff solutions of the Pareto front, decision makers can select specific configurations depending on the power demand and on economic or environmental restrictions.
Investigation on Process Parameters of EN-08 Steel by Using DoE and Multi-Objective Genetic Algorithm Approach
Published in Ganesh M. Kakandikar, Dinesh G. Thakur, Nature-Inspired Optimization in Advanced Manufacturing Processes and Systems, 2020
Syed Anjum Alam, Ashish Goyal, Manish Dadhich
In the present study, the effect of process parameters on response parameters of CNC milling machining process was investigated. The feed rate, speed, and depth of cut process were selected with three levels each. The cutting time and surface roughness were investigated in the present study. The following conclusions have been drawn: Using mean data analysis, the rank of each factor for cutting time and surface roughness has been analyzed. The speed is found to be the most significant parameter for surface roughness, and the depth of cut is found to be the most significant parameter for cutting time. The regression equation has also been generated for both the response variables.The optimal solution for each factor was determined and discussed for showing the quality of results. The predicted and experimental results are shown in Table 1.11. The experimental values are in good agreement with the predicted values The optimization of model equations was performed for cutting time and surface roughness using MOGA technique. It was useful to predict the role of optimum solution for milling machining process. The Pareto front results are obtained by using the MATLAB tool.In the present study, mathematical modeling and optimization of process parameters were made for cutting time and surface roughness. This work can be extended to other response variables, i.e., tool wear rate, dimensional deviation, overcut, etc. Also, other parameters can be used to have a more insight into the process.
Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems
Published in Engineering Optimization, 2022
Regina S. Burachik, C. Yalçın Kaya, Mohammed Mustafa Rizvi
Algorithms 1–7 are described in Section 3 by means of two-, three- and four-objective integer and mixed-integer programming problems. Test problems 1–4 are tested and provided in the online supplemental data. These problems are designed in such a way that the number of points in the Pareto front is finite and that they can be interpreted (or easily visualized) geometrically, so that the weak Pareto points are known prior to computations. These known weak Pareto, or weak efficient, points are referred to as being exact. One of the aims is to understand the capabilities of Algorithms 1–6 in approximating the set of exact weak Pareto points. The task of approximating a Pareto front is particularly challenging for the three- and four-objective cases. Algorithm 7 is tested on a challenging real-life problem, namely rocket injector design, which has four objective functions to minimize simultaneously.
Performance- and cost-based robust design optimization procedure for typical foundations for wind turbine
Published in International Journal of Geotechnical Engineering, 2020
Nadarajah Ravichandran, Shweta Shrestha
The Pareto front is a plot of non-dominated design sets that show a trade-off relationship between two the objectives: cost and variation in the response. That is, one objective cannot be improved without compromising the other. The concept of Pareto optimality is to find the best solution of the multi-objective problem for the given limitations in the objectives. In the Pareto front for the foundation design, the total cost measures the cost efficiency and the standard deviation of the differential settlement measures the robustness. The term robustness is defined as the insensitivity of response of the system when it is subjected to an adverse condition such as variation in random variables. A smaller standard deviation of the differential settlement means a higher robustness. Usually, an engineer would prefer to achieve a higher level of robustness with lower cost. However, this is not possible due to the trade-off relationship between the cost and robustness measures. For comparing the cost and robustness of the three foundations, the Pareto fronts for each foundation is are plotted in the same graph. The comparison will be useful for selecting foundation type for a given set of robustness and cost limitation.
Multi-objective maintenance strategy for in-service corroding pipelines using genetic algorithms
Published in Structure and Infrastructure Engineering, 2018
The Pareto front in the multi-objective optimisation is defined as a tradeoff front where a series of solutions are non-dominated with respect to each other in terms of the objectives. A solution is dominated by another solution if the latter is better than the former in at least one objective and no worse than the former in all the other objectives. The Pareto front ranking involves first assigning the non-dominated solutions in the population as a rank of one (i.e. the first front) and then removes such solutions from the population; the non-dominated solutions in the remaining population are subsequently identified and assigned to the second Pareto front, and such a process is repeated until all solutions in the population are assigned appropriate ranks. Fitness values are then assigned to different solutions.