Trade-off analysis approach for interactive nonlinear multiobjective optimization

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

Multi-objectives optimization problems are often solved constructing the Pareto front and applying a decision-making strategy to select the preferred solution among the Pareto-optimal solutions. With the aim to reduce the computational effort in multi-objective optimization problems, this paper presents a procedure for the direct evaluation of the preferred updated model, without the need to evaluate the whole Pareto front. For this purpose, the objective function to minimize is defined as the distance between a candidate point and the equilibrium point in the objective function space. The choice of the criterion of the minimum distance from the equilibrium point comes from a preliminary study carried out to assess the performances of different selection criteria. The robustness and the efficiency of the proposed procedure are assessed through the comparison with the results obtained from the estimation of the Pareto-optimal solutions and the subsequent selection of the preferred one for two numerical case studies. The proposed procedure is finally applied to the calibration of a complex FE model with respect to experimental modal data. Results show that the proposed procedure is effective and considerably reduces the computational effort. Moreover, the procedure is able to directly estimate the optimal weighting factor that allows to know the relative importance between the selected objectives and can be used to solve the multi-objective optimization with the weighed sum method.

As a main carrier mode for the sustainable development of the construction industry in China, prefabricated building may lead to problems such as cost overruns, project delays, and waste of resources due to unreasonable selection of prefabricated components. Therefore, we quantitatively analyze the contribution rate of quality optimization of prefabricated components using QFD-SEM. Under the constraints of prefabrication rate, quality optimization contribution rate, and expected values of various sub-goals, we propose a multi-objective optimization method for prefabricated component combinations based on cost, duration, and carbon emissions. By using NSGA-II to solve the model, we can obtain a set of optimal Pareto solutions for prefabricated component combinations. Based on the optimal Pareto solution set, we establish a multi-objective evaluation model using simulated annealing optimization projection tracing method, and select the optimal prefabricated component combination solution according to the projected eigenvalues of the solutions. An empirical study is conducted using an eleven-story framed building in Shenzhen, Guangdong Province, China as a case study. The results show that: (1) Using this method, optimal solutions can be obtained in an unbounded solution space, with the optimal solution having advantages over both fully cast-in-place and fully prefabricated solutions. Compared to the fully cast-in-place solution, the duration and carbon emissions are reduced by 36.62% and 12.74% respectively, while compared to the fully prefabricated solution, costs are reduced by 4.15%. (2) There is a certain negative correlation between the cost of prefabricated component combinations and duration, carbon emissions, and quality optimization, while there is a certain positive correlation with the prefabrication rate. (3) The size of the optimal projection direction vector based on the optimization objectives indicates that carbon emissions have the greatest impact on the evaluation results of the solutions.

In sheet metal forming most of the problems are multi objective problems, generally characterized by conflicting objectives. The definition of proper parameters aimed to prevent both wrinkles and fracture is a typical example of an optimization problem in sheet metal forming characterized by conflicting goals. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an industrial environment. Thus, the design parameters calibration, accomplishing all the objectives, is difficult and sometimes unsuccessful. In order to overcome this drawback a multi-objectives optimization procedure based on Pareto optimal solution search techniques seems a very attractive approach to deal with sheet metal forming processes design. In this paper, an integration between numerical simulations, response surface methodology and Pareto optimal solution search techniques was applied in order to design a rectangular deep drawing process. In particular, the initial blank shape and the blank holder force history were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid wrinkling occurrence. The steps of the optimization procedure include: 1) application of Central Composite Design (CCD) for the identification of the necessary data over the domain of variation of the design variables; 2) numerical simulations of the samples identified by CCD; 3) development of a response surface model to interpret the final objectives as functions of the design variables; 4) Pareto optimal solution analysis to reach the most performing design variables. The final aim is to develop a predictive tool able to identify a sort of process window for the analyzed process also minimizing the computational effort in particular with respect to mono-objective optimization techniques or traditional trial and error methods. Many possible technological scenarios were investigated by the implemented procedure and a set of reliable solutions, i.e. able to satisfy different design requirements, were obtained.

MOEA/UE: A novel multi-objective evolutionary algorithm using a uniformly evolving scheme

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin.

ABSTRACTThe paper targets an optimal soil cutting operation by considering economic and productive aspects. Three realistic objectives and three problem-specific constraints are developed, and the optimization problem is solved using a hybrid evolutionary multi-objective optimization (EMO) technique. In this technique, a set of non-dominated solutions is generated by using an existing EMO technique, and then a few of them are selected for local search using the -constraint method. These selected solutions are used for starting independent local searches using fmincon solver of Matlab. Results demonstrate that the local searches have improved the non-dominated solutions a little, thereby suggesting a closeness of evolved solutions from EMO technique with true Pareto-optimal (PO) solutions. The PO solutions are further validated using experimental data from the literature. Overall, this study offers a platform to choose an appropriate solution from the set of PO solutions. Moreover, the post-optimal analysis demonstrates the commonality principle of few decision variables, which is followed by all PO solutions. The rest of the decision variables decipher important relationships that are responsible for trade-off among the PO solutions. The relationships are later used for preparing guidelines for a practitioner in selecting an appropriate solution for the optimal operation.

Decision making for probabilistic fatigue inspection planning based on multi-objective optimization

In the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

The two primary goals of a multi-objective evolutionary algorithm (MOEA) for solving multi-objective optimization problems are to search as much non-dominated solutions as possible towards the true Pareto front and to maintain diversity of Pareto optimal solutions along tradeoff curves. This study presents a new hybrid MOEA, the niched Pareto tabu search combined with genetic algorithm (NPTSGA), to find Pareto-optimal solutions to multi-objective optimization problems. The NPTSGA is developed on the thoughts of integrating genetic algorithm (GA) with the improved tabu search (TS) based MOEA, niched Pareto tabu search (NPTS). The proposed NPTSGA is then tested through a simple test example and compared with other two techniques, NPTS and niched Pareto genetic algorithm (NPGA). Computational results indicate that the proposed NPTSGA is an efficient and effective method for solving multi-objective problems, while keeping the balance between the intensification of non-domination to the true Pareto-optimal solutions (TPS) and the diversification of the near Pareto-optimal solutions (NPS) along the tradeoff curves.

Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs

Most practical problems are formulated as multiobjective optimization problems (MOP) so as to meet the diversified demands of a decision maker. Usually, there is a trade-off relation among objective functions, and thus there does not necessarily exist the solution that optimizes all objective functions simultaneously in MOP. Therefore, Pareto optimal solution is used as a definition of solution to MOP. Recently, evolutionary algorithms have been developed remarkably in order to obtain approximate solutions to optimization problems. Particularly, multiobjective genetic algorithms (MOGA) have been developed for generating Pareto optimal solutions. However, there are two problems in MOGA: how to assign the fitness to individuals, and how to keep the diversification of individuals. Many existing MOGAs have made an effort in order to overcome these problems, and so does this paper. First, this paper suggests a fitness function in MOGA using generalized data envelopment analysis (GDEA) which was suggested for evaluating the relative efficiency of individuals under several items of assessment management science. It is shown that the GDEA method can approximate Pareto optimal solutions more effectively and faster than the ranking method which is mostly used in MOGA, and generate well-distributed Pareto optimal solutions. Furthermore, this paper suggests the aspiration-level based GDEA method to generate the most interesting part (not the whole Pareto optimal solutions) to an aspiration level of decision maker for choosing a final solution from many Pareto optimal solutions. Finally, this paper illustrates the effectiveness of the methods using GDEA through several numerical examples.

Municipalities across the United States face the challenge of sanitary sewer overflows (SSOs), events which pose serious public health and environmental problems. SSOs are unintentional discharges of untreated sewage from the sewer system that can occur as a result of rain derived infiltration and inflow (RDII). SSOs can be reduced by decreasing RDII into the collection system, increasing conveyance capacity, and lessening peak flow through detention storage facilities. However, the sheer length of sanitary sewer systems makes the implementation of these controls very costly. Thus, a novel approach is required to a posteriori design cost-effective rehabilitation options. This study describes a multiobjective evolutionary optimization approach to design a rehabilitation strategy for SSOs reduction in the eastern subsewershed of the San Antonio Water System (SAWS) sewer network. The subsewershed consists of 3,304 conduits connected via 3,155 manholes to form a network that is 160.8 miles long and services an area covering 20.4 square miles with an approximate population of 36,000 inhabitants. The hydraulic behavior of the system is simulated using the EPA Storm Water Management Model (EPA-SWMM) hydraulic model, and the number of SSOs is calculated as the number of nodes that oveflow during the 5 year–6 hours design storm. The optimization method utilized was the Nondominated Sorting Genetic Algorithm (NSGA II) to generate near Pareto-optimal solutions that express tradeoffs between the number of SSOs and cost. The NSGA II was implemented in JAVA, where each individual is represented as a set of vectors that is composed of three sets of genes. The decision variables include the number of pipe segments to be replaced, the location of the first link to be replaced, and the amount of commercial diameter increase from existing pipe diameter. The use of the optimization approach is expected to generate more efficient solutions in comparison to typical engineering approaches that look into solving a localized SSOs problems in sanitary sewer networks.

Purpose This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions. Design/methodology/approach In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared. Findings The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches both for the problems of design and control. Originality/value This paper represents and investigates different MOO approaches for design and control of electrotechnological systems.

A multi-objective optimal operation model of water-sedimentation-power in reservoir is established with power-generation, sedimentation and water storage taken into account. Moreover, the inertia weight self-adjusting mechanism and Pareto-optimal archive are introduced into the particle swarm optimization and an improved multi-objective particle swarm optimization (IMOPSO) is proposed. The IMOPSO is employed to solve the optimal model and obtain the Pareto-optimal front. The multi-objective optimal operation of Wanjiazhai Reservoir during the spring breakup was investigated with three typical flood hydrographs. The results show that the former method is able to obtain the Pareto-optimal front with a uniform distribution property. Different regions (A, B, C) of the Pareto-optimal front correspond to the optimized schemes in terms of the objectives of sediment deposition, sediment deposition and power generation, and power generation, respectively. The level hydrographs and outflow hydrographs show the operation of the reservoir in details. Compared with the non-dominated sorting genetic algorithm-II (NSGA-II), IMOPSO has close global optimization capability and is suitable for multi-objective optimization problems.