Hypervolume Indicator Gradient Ascent Multi-objective Optimization

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

During recent decades, evolutionary algorithms have been widely studied in optimization problems. The multi-objective whale optimization algorithm based on multi-leader guiding is proposed in this paper, which attempts to offer a proper framework to apply whale optimization algorithm and other swarm intelligence algorithms to solving multi-objective optimization problems. The proposed algorithm adopts several improvements to enhance optimization performance. First, search agents are classified into leadership set and ordinary set by grid mechanism, and multiple leadership solutions guide the population to search the sparse spaces to achieve more homogeneous exploration in per iteration. Second, the differential evolution and whale optimization algorithm are employed to generate the offspring for the leadership and ordinary solutions, respectively. In addition, a novel opposition-based learning strategy is developed to improve the distribution of the initial population. The performance of the proposed algorithm is verified in contrast to 10 classic or state-of-the-arts algorithms on 20 bi-objective and tri-objective unconstrained problems, and experimental results demonstrate the competitive advantages in optimization quality and convergence speed. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned experiments have indicated that the proposed algorithm is comparatively effective and efficient.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization

Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

Evolutionary algorithms have been widely used to tackle multi-objective optimization problems. Despite many successful applications there is a lack of theoretical knowledge on how and why this type of algorithm works particularly well for multi-objective problems. This special issue presents current advances to the theoretical understanding of evolutionary algorithms for multi-objective optimization. It comprises four very high quality papers which have been selected via a rigorous reviewing process. The first paper “On the Effect of Populations in Evolutionary Multi-Objective Optimisation” by Oliver Giel and Per Kristian Lehre studies the basic question whether a population is provably useful to compute the whole Pareto front of a multi-objective optimization problem. They compare restart strategies of several single-objective approaches based on one individual to a natural multi-objective approach using a population. Their analyses point out the benefits of the multi-objective evolutionary algorithm in a rigorous way. Using illustrative example functions they provide not only proven results but also a good intuition about why population-based approaches can outperform individual-based approaches in multi-objective optimization. The paper “Exploring the Runtime of an Evolutionary Algorithm for the Multi-Objective Shortest Path Problem” by Christian Horoba examines the behavior of evolutionary algorithms for the classical NP-hard multi-objective shortest path problem. The author considers an evolutionary approach based on -dominance and proves that this algorithm constitutes a fully polynomial-time randomized approximation scheme (FPRAS) for the problem. The algorithm achieves this by mimicking a problemspecific algorithm for that problem. This provides general insight into why evolutionary algorithms can perform well for problems that allow for efficient problem-specific algorithms. Hypervolume-based algorithms have become very popular in evolutionary multiobjective optimization. In the paper, “An Efficient Algorithm for Computing Hypervolume Contributions,” Karl Bringmann and Tobias Friedrich present a faster algorithm for determining the individual with the smallest hypervolume contribution in a given population. Furthermore, they study the problem of removing λ > 1 individuals with the smallest hypervolume contribution from a given population and present an elegant and fast method to carry out this task.

Evolutionary algorithm has gained a worldwide popularity among multi-objective optimization. The paper proposes a self-adaptive evolutionary algorithm (called SEA) for multi-objective optimization. In the SEA, the probability of crossover and mutation, P cand P m, are varied depending on the fitness values of the solutions. Fitness assignment of SEA realizes the twin goals of maintaining diversity in the population and guiding the population to the true Pareto Front; fitness value of individual not only depends on improved density estimation but also depends on non-dominated rank. The density estimation can keep diversity in all instances including when scalars of all objectives are much different from each other. SEA is compared against the Non-dominated Sorting Genetic Algorithm (NSGA-II) on a set of test problems introduced by the MOEA community. Simulated results show that SEA is as effective as NSGA-II in most of test functions, but when scalar of objectives are much different from each other, SEA has better distribution of non-dominated solutions.

Evolutionary algorithms have been widely used to solve multi-objective optimization problems. Usually, the final population of an evolutionary algorithm is used as the output of multi-objective optimization. However, a current new trend is to select a pre-specified number of solutions from an unbounded external archive (UEA) as the final output of multi-objective optimization. Some subset selection methods have been proposed in the literature such as hypervolume-based and IGD-based selection. Recently, a distance-based subset selection (DSS) method was proposed for efficient subset selection from a large external archive. Whereas DSS efficiently finds a set of uniformly distributed solutions, it has some difficulties in the handling of solutions in the UEA as we demonstrate in this paper. To improve the performance of the DSS method, we propose a modified DSS method based on the IGD+ distance instead of the Euclidean distance. Experimental results on various benchmark problems show that the modified DSS method performs better than or equal to the original DSS method on most test problems.

An innovative method for the automatic design of optical systems is presented and verified. The proposed method is based on a multi-objective evolutionary memetic optimization algorithm. The multi-objective approach simultaneously, but separately, addresses the image quality, tolerance, and complexity of the system. The memetic technique breaks down the search for optical designs in to three different parts or phases: optical glass selection, exploration, and exploitation. The optical glass selection phase defines the most appropriate set of glasses for the system under design. The glass selection phase limits the available glasses from hundreds to just a few, drastically reducing the design space and significantly increasing the efficiency of the automatic design method. The exploration phase is based on an evolutionary algorithm (EA), more specifically, on a problem-tailored generalized extremal optimization (GEO) algorithm, named Optical GEO (O-GEO). The new EA incorporates many features customized for lens design, such as optical system codification and diversity operators. The trade-off systems found in the exploration phase are refined by a local search, based on the damped least square method in the exploitation phase. As a result, the method returns a set of trade-off solutions, generating a Pareto front. Our method delivers alternative and useful insights for the compromise solutions in a lens design problem. The efficiency of the proposed method is verified through real-world examples, showing excellent results for the tested problems.

For problems involving uncertainties in design variables and parameters, a bi-objective evolutionary algorithm (EA) based approach to design optimization using evidence theory is proposed and implemented in this paper. In addition to a functional objective, a plausibility measure of failure of constraint satisfaction is minimized. Despite some interests in classical optimization literature, this is the first attempt to use evidence theory with an EA. Due to EA's flexibility in modifying its operators, nonrequirement of any gradient, its ability to handle multiple conflicting objectives, and ease of parallelization, evidence-based design optimization using an EA is promising. Results on a test problem and two engineering design problems show that the modified evolutionary multi-objective optimization algorithm is capable of finding a widely distributed trade-off frontier showing different optimal solutions corresponding to different levels of plausibility failure limits. Furthermore, a single-objective evidence-based EA is found to produce better optimal solutions than a previously reported classical optimization algorithm. Furthermore, the use of a graphical processing unit (GPU) based parallel computing platform demonstrates EA's performance enhancement around 160–700 times in implementing plausibility computations. Handling uncertainties of different types are getting increasingly popular in applied optimization studies and this EA based study is promising to be applied in real-world design optimization problems.

In recent years, multi-objective evolutionary optimization algorithms have shown success in different areas of research. Due to their efficiency and power, many researchers have concentrated on adapting evolutionary algorithms to generate Pareto solutions. This paper proposes a new memetic adaptive multi-objective evolutionary algorithm that is based on a three-term backpropagation network (MAMOT). This algorithm is an automatic search method for optimizing the parameters and performance of neural networks, and it relies on the use of the adaptive non-dominated sorting genetic algorithm-II integrated with the backpropagation algorithm, being used as a local search method. The presented MAMOT employs a self-adaptive mechanism toward improving the performance of the proposed algorithm and a local optimizer improving all the individuals in a population in order to obtain better accuracy and connection weights. In addition, it selects an appropriate number of hidden nodes simultaneously. The proposed method was applied to 11 datasets representing pattern classification problems, including two-class, multi-class and complex data reflecting real problems. Experiments were performed, and the results indicated that the proposed method is viable in pattern classification tasks compared to a multi-objective genetic algorithm based on a three-term backpropagation network (MOGAT) and some of the methods mentioned in the literature. The statistical analysis results of the t test and Wilcoxon signed-ranks test also show that the performance of the proposed method is significantly better than MOGAT.

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

Due to the conflict between reducing cost and improving water supply performance, how to select the appropriate pipe diameter is a current challenge. In this paper, the problem is transformed into a multi-objective optimization problem, and the evolutionary genetic optimization algorithm is used to solve the problem to determine the optimal selection of pipe diameter in the pipe network. To solve this problem, the evolutionary genetic algorithm was coupled with EPANET hydraulic simulation software in Python environment. The results show that NSGA-II and NSGA-III perform better in two typical case tests. Moreover, the increase of the objective functions will lead to an increase in the amount of data in the optimal solution set, and will affect the optimal value of each objective function. That shows that the balance between the economy and reliability of water supply can be successfully found by coupling the hydraulic model and the multi-objective optimization algorithm, which can provide an auxiliary decision for enterprises.

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

Most global wind resources are found in water depths exceeding 60 meters, where using bottom-mounted structures is challenging and costly. Thus, increased the studies on floating offshore wind turbine (FOWT) solutions characterized by complex dynamics between the floating structures and turbines. Nowadays, one key challenge is designing optimum mooring arrangements for large-scale FOWT. A meta-heuristic solution is recommended to solve a complex optimization problem, such as the mooring arrangement of a floating wind turbine. Among these, the Evolutionary Algorithms (EA) use mechanisms inspired by biological evolution. Genetic Algorithm (GA) is a multi-objective search and optimization algorithm based on the concept of Darwin’s theory of evolution, and it belongs to the class of Evolutionary Algorithms. It combines the idea of survival of the fittest with randomized information exchange. Based on the literature, multi-objective optimization algorithms, such as the GA, are commonly used with hydrostatic and frequency-domain models, which are less accurate than a time-domain model for optimization purposes of FOWT. This work addresses the optimization of the mooring system of a FOWT using time-domain simulations in OpenFAST. An in-house code is developed to handle calculations on OpenFAST and apply GA to find the optimal mooring arrangements for specific design variables meeting predefined multi-objectives, respecting all specific constraints for the FOWT. Finally, the optimized arrangements are checked against Ultimate Limit State (ULS) and Accidental Limit State (ALS), performed for the mooring system in damaged condition. The developed optimization process is applied to the UMaine VolturnUS-S semisubmersible platform to maximize power quality and minimize the costs of the lines.

PSE (Parameter Sweep Experiments) applications represent a relevant class of computational applications in science, engineering and industry. These applications involve many computational tasks that are both resource-intensive and independent. For this reason, these applications are suited for Cloud environments. In this sense, Cloud autoscaling approaches are aimed to manage the execution of different kinds of applications on Cloud environments. One of the most recent approaches proposed for autoscaling PSE applications is MIA, which is based on the multi-objective evolutionary algorithm NSGA-III. We propose to endow MIA with other multi-objective optimization algorithms, to improve its performance. In this respect, we consider two well-known multi-objective optimization algorithms named SMS-EMOA and SMPSO, which have significant mechanic differences with NSGA-III. We evaluate MIA endowed with each of these algorithms, on three real-world PSE applications, considering resources available in Amazon EC2. The experimental results show that MIA endowed with each of these algorithms significantly outperforms MIA based on NSGA-III.