A New Decomposition-Based Many-Objective Algorithm Based on Adaptive Reference Vectors and Fractional Dominance Relation

Most of the existing evolutionary algorithms to deal with many-objective problems are based on the enhancing of selection strategy. Among them, the reference vector-guided evolutionary algorithm (RVEA) achieves excellent performance. In this paper, a new search engine is combined with RVEA to achieve further performance enhancement of the differential evolutionary (DE) algorithm. In the optimization process of differential evolution algorithm on many-objective problems, improving convergence and maintaining diversity are two different optimization directions, and it is usually difficult to maintain a balance between them. To solve this problem, a new search engine based on DE is proposed. The proposed search engine is implemented based on a cooperative scheme of local and global search strategies. In the local search, the population is divided into several sub-populations, each of which evolves independently using the proposed mutation strategy. The distance between the individuals in each sub-population is relatively close. Therefore, it has a strong exploitation capability, and will not make the population lose diversity. Meanwhile, the selection strategy of RVEA enables the population to maintain diversity, and the DE/rand/1 utilized in global search is sufficient to keep a strong exploration capability. Therefore, the proposed approach can achieve a good balance between exploration and exploitation. The experimental results show that the proposed algorithm performs well in many-objective optimizations up to more than 10 objectives.

A many-objective evolutionary algorithm based on rotation and decomposition

It is highly desirable to adapt the reference vectors to unknown Pareto fronts (PFs) in decomposition-based evolutionary many-objective optimization. While adapting the reference vectors enhances the diversity of the achieved solutions, it often decelerates the convergence performance. To address this dilemma, we propose to adapt the reference vectors and the scalarizing functions in a coordinated way. On the one hand, the adaptation of the reference vectors is based on a local angle threshold, making the adaptation better tuned to the distribution of the solutions. On the other hand, the weights of the scalarizing functions are adjusted according to the local angle thresholds and the reference vectors’ age, which is calculated by counting the number of generations in which one reference vector has at least one solution assigned to it. Such coordinated adaptation enables the algorithm to achieve a better balance between diversity and convergence, regardless of the shape of the PFs. Experimental studies on MaF, DTLZ, and DPF test suites demonstrate the effectiveness of the proposed algorithm in solving problems with both regular and irregular PFs.

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

The low frequency vibration of the vehicle in motion has a great influence on the ride comfort of occupants. The research on the vibration response characteristics of human body plays a great role in analyzing and improving ride comfort. The purpose of this study was to investigate the parameter identification of seated human body dynamic model. A seven-degree-of-freedom (DOF) lumped parameter model was established to describe the vibration response characteristics of human body. The derivation processes of apparent mass (AM) and seat to head transmissibility (STHT) were performed. After the theoretical calculation of the human body vibration characteristics, we used several different evolutionary algorithms to identify the 23 parameters of the model, including the mass, stiffness and damping parameters. By comparing the results of the five optimization algorithms and comprehensively analyzing the convergence and distribution of the non-dominated solution set, we found that the reference vector guided evolutionary algorithm (RVEA) shows good competitiveness in solving many-objective optimization problem (MaOP), that is, parameter identification of seated human body model in this paper. The AM and STHT calculated by model identification were compared with their measured by experiment. The result shows that the selected seven-DOF model can well describe the vertical vibration characteristics of seated human body and the identification method used in this paper can accurately identify the parameters of lumped parameter model, which provides convenience for the establishment of a complete “road-vehicle-seat-human body” system dynamic model.

We propose a surrogate-assisted reference vector adaptation (SRVA) method to\nsolve expensive multi- and many-objective optimization problems with various\nPareto front shapes. SRVA is coupled with a multi-objective Bayesian\noptimization (MBO) algorithm using reference vectors for scalarization of\nobjective functions. The Kriging surrogate models for MBO is used to estimate\nthe Pareto front shape and generate adaptive reference vectors uniformly\ndistributed on the estimated Pareto front. We combine SRVA with expected\nimprovement of penalty-based boundary intersection as an infill criterion for\nMBO. The proposed algorithm is compared with two other MBO algorithms by\napplying them to benchmark problems with various Pareto front shapes.\nExperimental results show that the proposed algorithm outperforms the other two\nin the problems whose objective functions are reasonably approximated by the\nKriging models. SRVA improves diversity of non-dominated solutions for these\nproblems with continuous, discontinuous, and degenerated Pareto fronts.\nBesides, the proposed algorithm obtains much better solutions from early stages\nof optimization especially in many-objective problems.\n

A diversity indicator based on reference vectors for many-objective optimization

Hybrid flow shop scheduling (HFS) is an on sought problem modelling for production manufacturing. Due to its impact on productivity, researchers from different backgrounds have been attracted to solve its optimum solution. The HFS is a complex dilemma and provides ample solutions, thus inviting researchers to propose niche optimization methods for the problem. Recently, researchers have moved on to multi-objective solutions. In real-world situations, HFS is known for multi-objective problems, and consequently, the need for optimum solutions in multi-objective HFS is a necessity. Regarding sustainability topic, energy utilization is mainly considered as one of the objectives, including the common makespan criteria. This paper presents the existing multi-objective approach for solving energy utilization and makespan problems in HFS scheduling using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), and a comparison to other optimization models was subjected for analysis. The model was compared with the most sought algorithm and latest multi-objective algorithms, Strength Pareto Evolutionary Algorithm 2 (SPEA -II), Multi-Objective Algorithm Particle Swarm Optimization (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The research interest starts with problem modelling, followed by a computational experiment with an existing multi-objective approach conducted using twelve HFS benchmark problems. Then, a case study problem is presented to assess all models. The numerical results showed that the NSGA-III obtained 50% best overall for distribution performance metrics and 42% best in convergence performance metrics for HFS benchmark problems. In addition, the case study results show that NSGA-III obtained the best overall convergence and distribution performance metrics. The results show that NSGA-III can search for the best fitness solution without compromising makespan and total energy utilization. In the future, these multi-objective algorithms’ potential can be further investigated for hybrid flow shop scheduling problems.

Decomposition-based evolutionary algorithm with dual adjustments for many-objective optimization problems

An information entropy-driven evolutionary algorithm based on reinforcement learning for many-objective optimization

An adaptive clustering-based evolutionary algorithm for many-objective optimization problems

Deep and wide search assisted evolutionary algorithm with reference vector guidance for many-objective optimization

The design of Renewable Energy Power Plants (REPPs) is crucial not only for the investments' performance and attractiveness measures, but also for the maximization of resource (source) usage (e.g. sun, water, and wind) and the minimization of raw materials (e.g. aluminum: Al, cadmium: Cd, iron: Fe, silicon: Si, and tellurium: Te) consumption. Hence, several appropriate and satisfactory Multi-Objective Problems (MOPs) are mandatory during the REPPs' design phases. MOPs related tasks can only be managed by very well organized knowledge acquisition on all REPPs' design equations and models. The proposed MOPs need to be solved with one or more multi-objective algorithm, such as Multi-Objective Evolutionary Algorithms (MOEAs). In this respect, the first aim of this research study is to start gathering knowledge on the REPPs' MOPs. The second aim of this study is to gather detailed information about all MOEAs and available free software tools for their development. The main contribution of this research is the initialization of a proposed multi-objective evolutionary algorithm knowledge acquisition system for renewable energy power plants (MOEAs-KAS-F-REPPs) (research and development loopwise process: develop, train, validate, improve, test, improve, operate, and improve). As a simple representative example of this knowledge acquisition system research with two selective and elective proposed standard objectives (as test objectives) and eight selective and elective proposed standard constraints (as test constraints) are generated and applied as a standardized MOP for a virtual small hydropower plant design and investment. The maximization of energy generation (MWh) and the minimization of initial investment cost (million €) are achieved by the Multi-Objective Genetic Algorithm (MOGA), the Niched Sharing Genetic Algorithm/Non-dominated Sorting Genetic Algorithm (NSGA-I), and the NSGA-II algorithms in the Scilab 6.0.0 as only three standardized MOEAs amongst all proposed standardized MOEAs on two desktop computer configurations (Windows 10 Home 1709 64 bits, Intel i5-7200 CPU @ 2.7 GHz, 8.00 GB RAM with internet connection and Windows 10 Pro, Intel(R) Core(TM) i5 CPU 650 @ 3.20 GHz, 6,00 GB RAM with internet connection). The algorithm run-times (computation time) of the current applications vary between 20.64 and 59.98 seconds.

In the last decade, numerous multi/many-objective evolutionary algorithms (MOEAs) have been proposed to handle multi/many-objective problems (MOPs) with challenges such as discontinuous Pareto Front (PF), degenerate PF, etc. MOEAs in the literature can be broadly divided into three categories based on the selection strategy employed such as dominance, decomposition, and indicator-based MOEAs. Each category of MOEAs have their advantages and disadvantages when solving MOPs with diverse characteristics. In this work, we propose a Hybrid Selection based MOEA, referred to as HS-MOEA, which is a simple yet effective hybridization of dominance, decomposition and indicator-based concepts. In other words, we propose a new environmental selection strategy where the Pareto-dominance, reference vectors and an indicator are combined to effectively balance the diversity and convergence properties of MOEA during the evolution. The superior performance of HS-MOEA compared to the state-of-the-art MOEAs is demonstrated through experimental simulations on DTLZ and WFG test suites with up to 10 objectives.

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.