Evolutionary Dynamic Multi-Objective Optimisation : A survey

Peer reviewedPostprin

Direct transcription of low-thrust trajectories with finite trajectory elements

This paper presents a novel approach to the design of Low-Thrust trajectories, based on a first order approximated analytical solution of Gauss planetary equations. This analytical solution is shown to have a better accuracy than a second-order explicit numerical integrator and at a lower computational cost. Hence, it can be employed for the fast propagation of perturbed Keplerian motion when moderate accuracy is required. The analytical solution was integrated in a direct transcription method based on a decomposition of the trajectory into direct finite perturbative elements (DFPET). DFPET were applied to the solution of two-point boundary transfer problems. Furthermore the paper presents an example of the use of DFPET for the solution of a multiobjective trajectory optimisation problem in which both the total ∆V and transfer time are minimized with respect to departure and arrival dates. Two transfer problems were used as test cases: a direct transfer from Earth to Mars and a spiral from a low Earth orbit to the International Space Station

Non-weighted aggregate evaluation function of multi-objective optimization for knock engine modeling

In decision theory, the weighted sum model (WSM) is the best known Multi-Criteria Decision Analysis (MCDA) approach for evaluating a number of alternatives in terms of a number of decision criteria. Assigning weights is a difficult task, especially if the number of criteria is large and the criteria are very different in character. There are some problems in the real world which utilize conflicting criteria and mutual effect. In the field of automotive, the knocking phenomenon in internal combustion or spark ignition engines limits the efficiency of the engine. Power and fuel economy can be maximized by optimizing some factors that affect the knocking phenomenon, such as temperature, throttle position sensor, spark ignition timing, and revolution per minute. Detecting knocks and controlling the above factors or criteria may allow the engine to run at the best power and fuel economy. The best decision must arise from selecting the optimum trade-off within the above criteria. The main objective of this study was to proposed a new Non-Weighted Aggregate Evaluation Function (NWAEF) model for non-linear multi-objectives function which will simulate the engine knock behavior (non-linear dependent variable) in order to optimize non-linear decision factors (non-linear independent variables). This study has focused on the construction of a NWAEF model by using a curve fitting technique and partial derivatives. It also aims to optimize the nonlinear nature of the factors by using Genetic Algorithm (GA) as well as investigate the behavior of such function. This study assumes that a partial and mutual influence between factors is required before such factors can be optimized. The Akaike Information Criterion (AIC) is used to balance the complexity of the model and the data loss, which can help assess the range of the tested models and choose the best ones. Some statistical tools are also used in this thesis to assess and identify the most powerful explanation in the model. The first derivative is used to simplify the form of evaluation function. The NWAEF model was compared to Random Weights Genetic Algorithm (RWGA) model by using five data sets taken from different internal combustion engines. There was a relatively large variation in elapsed time to get to the best solution between the two model. Experimental results in application aspect (Internal combustion engines) show that the new model participates in decreasing the elapsed time. This research provides a form of knock control within the subspace that can enhance the efficiency and performance of the engine, improve fuel economy, and reduce regulated emissions and pollution. Combined with new concepts in the engine design, this model can be used for improving the control strategies and providing accurate information to the Engine Control Unit (ECU), which will control the knock faster and ensure the perfect condition of the engine

A Data-Driven Evolutionary Transfer Optimization for Expensive Problems in Dynamic Environments

Many real-world problems are usually computationally costly and the objective functions evolve over time. Data-driven, a.k.a. surrogate-assisted, evolutionary optimization has been recognized as an effective approach for tackling expensive black-box optimization problems in a static environment whereas it has rarely been studied under dynamic environments. This paper proposes a simple but effective transfer learning framework to empower data-driven evolutionary optimization to solve dynamic optimization problems. Specifically, it applies a hierarchical multi-output Gaussian process to capture the correlation between data collected from different time steps with a linearly increased number of hyperparameters. Furthermore, an adaptive source task selection along with a bespoke warm staring initialization mechanisms are proposed to better leverage the knowledge extracted from previous optimization exercises. By doing so, the data-driven evolutionary optimization can jump start the optimization in the new environment with a strictly limited computational budget. Experiments on synthetic benchmark test problems and a real-world case study demonstrate the effectiveness of our proposed algorithm against nine state-of-the-art peer algorithms

Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq); (ii) Coordination for the Improvement of Higher Education (CAPES) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese)

Vector Autoregressive Evolution for Dynamic Multi-Objective Optimisation

Dynamic multi-objective optimisation (DMO) handles optimisation problems with multiple (often conflicting) objectives in varying environments. Such problems pose various challenges to evolutionary algorithms, which have popularly been used to solve complex optimisation problems, due to their dynamic nature and resource restrictions in changing environments. This paper proposes vector autoregressive evolution (VARE) consisting of vector autoregression (VAR) and environment-aware hypermutation to address environmental changes in DMO. VARE builds a VAR model that considers mutual relationship between decision variables to effectively predict the moving solutions in dynamic environments. Additionally, VARE introduces EAH to address the blindness of existing hypermutation strategies in increasing population diversity in dynamic scenarios where predictive approaches are unsuitable. A seamless integration of VAR and EAH in an environment-adaptive manner makes VARE effective to handle a wide range of dynamic environments and competitive with several popular DMO algorithms, as demonstrated in extensive experimental studies. Specially, the proposed algorithm is computationally 50 times faster than two widely-used algorithms (i.e., TrDMOEA and MOEA/D-SVR) while producing significantly better results

Understanding knee points in bicriteria problems and their implications as preferred solution principles

A knee point is almost always a preferred trade-off solution, if it exists in a bicriteria optimization problem. In this article, an attempt is made to improve understanding of a knee point and investigate the properties of a bicriteria problem that may exhibit a knee on its Pareto-optimal front. Past studies are reviewed and a couple of new definitions are suggested. Additionally, a knee region is defined for problems in which, instead of one, a set of knee-like solutions exists. Edge-knee solutions, which behave like knee solutions but lie near one of the extremes on the Pareto-optimal front, are also introduced. It is interesting that in many problem-solving tasks, despite the existence of a number of solution methodologies, only one or a few of them are commonly used. Here, it is argued that often such common solution principles are knee solutions to a bicriteria problem formed with two conflicting goals of the underlying problem-solving task. The argument is illustrated on a number of tasks, such as regression, sorting, clustering and a number of engineering designs