Improved Solution Search Performance of Constrained MOEA/D Hybridizing Directional Mating and Local Mating

In this study, we propose an improvement to the direct mating method, a constraint handling approach for multi-objective evolutionary algorithms, by hybridizing it with local mating. Local mating selects another parent from the feasible solution space around the initially selected parent. The direct mating method selects the other parent along the optimal direction in the objective space after the first parent is selected, even if it is infeasible. It shows better exploration performance for constraint optimization problems with coupling NSGA-II, but requires several individuals along the optimal direction. Due to the lack of better solutions dominated by the optimal direction from the first parent, direct mating becomes difficult as the generation proceeds. To address this issue, we propose a hybrid method that uses local mating to select another parent from the neighborhood of the first selected parent, maintaining diversity around good solutions and helping the direct mating process. We evaluate the proposed method on three mathematical problems with unique Pareto fronts and two real-world applications. We use the generation histories of the averages and standard deviations of the hypervolumes as the performance evaluation criteria. Our investigation results show that the proposed method can solve constraint multi-objective problems better than existing methods while maintaining high diversity.Comment: Revised paper presented at ISMSI2023, 9pages, 8 figures (Online

Parallel Multi-Objective Evolutionary Algorithms: A Comprehensive Survey

Multi-Objective Evolutionary Algorithms (MOEAs) are powerful search techniques that have been extensively used to solve difficult problems in a wide variety of disciplines. However, they can be very demanding in terms of computational resources. Parallel implementations of MOEAs (pMOEAs) provide considerable gains regarding performance and scalability and, therefore, their relevance in tackling computationally expensive applications. This paper presents a survey of pMOEAs, describing a refined taxonomy, an up-to-date review of methods and the key contributions to the field. Furthermore, some of the open questions that require further research are also briefly discussed

A Pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods

Dynamic Multiobjectives Optimization with a Changing Number of Objectives

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Existing studies on dynamic multiobjective optimization (DMO) focus on problems with time-dependent objective functions, while the ones with a changing number of objectives have rarely been considered in the literature. Instead of changing the shape or position of the Pareto-optimal front/set (PF/PS) when having time-dependent objective functions, increasing or decreasing the number of objectives usually leads to the expansion or contraction of the dimension of the PF/PS manifold. Unfortunately, most existing dynamic handling techniques can hardly be adapted to this type of dynamics. In this paper, we report our attempt toward tackling the DMO problems with a changing number of objectives. We implement a dynamic two-archive evolutionary algorithm which maintains two co-evolving populations simultaneously. In particular, these two populations are complementary to each other: one concerns more about the convergence while the other concerns more about the diversity. The compositions of these two populations are adaptively reconstructed once the environment changes. In addition, these two populations interact with each other via a mating selection mechanism. Comprehensive experiments are conducted on various benchmark problems with a time-dependent number of objectives. Empirical results fully demonstrate the effectiveness of our proposed algorithm.Engineering and Physical Sciences Research Council (EPSRC)NSF

Evolutionary Algorithms for Static and Dynamic Multiobjective Optimization

Many real-world optimization problems consist of a number of conflicting objectives that have to be optimized simultaneously. Due to the presence of multiple conflicting ob- jectives, there is no single solution that can optimize all the objectives. Therefore, the resulting multiobjective optimization problems (MOPs) resort to a set of trade-off op- timal solutions, called the Pareto set in the decision space and the Pareto front in the objective space. Traditional optimization methods can at best find one solution in a sin- gle run, thereby making them inefficient to solve MOPs. In contrast, evolutionary algo- rithms (EAs) are able to approximate multiple optimal solutions in a single run. This strength makes EAs good candidates for solving MOPs. Over the past several decades, there have been increasing research interests in developing EAs or improving their perfor- mance, resulting in a large number of contributions towards the applicability of EAs for MOPs. However, the performance of EAs depends largely on the properties of the MOPs in question, e.g., static/dynamic optimization environments, simple/complex Pareto front characteristics, and low/high dimensionality. Different problem properties may pose dis- tinct optimization difficulties to EAs. For example, dynamic (time-varying) MOPs are generally more challenging than static ones to EAs. Therefore, it is not trivial to further study EAs in order to make them widely applicable to MOPs with various optimization scenarios or problem properties. This thesis is devoted to exploring EAs’ ability to solve a variety of MOPs with dif- ferent problem characteristics, attempting to widen EAs’ applicability and enhance their general performance. To start with, decomposition-based EAs are enhanced by incorpo- rating two-phase search and niche-guided solution selection strategies so as to make them suitable for solving MOPs with complex Pareto fronts. Second, new scalarizing functions are proposed and their impacts on evolutionary multiobjective optimization are exten- sively studied. On the basis of the new scalarizing functions, an efficient decomposition- based EA is introduced to deal with a class of hard MOPs. Third, a diversity-first- and-convergence-second sorting method is suggested to handle possible drawbacks of convergence-first based sorting methods. The new sorting method is then combined with strength based fitness assignment, with the aid of reference directions, to optimize MOPs with an increase of objective dimensionality. After that, we study the field of dynamic multiobjective optimization where objective functions and constraints can change over time. A new set of test problems consisting of a wide range of dynamic characteristics is introduced at an attempt to standardize test environments in dynamic multiobjective optimization, thereby aiding fair algorithm comparison and deep performance analysis. Finally, a dynamic EA is developed to tackle dynamic MOPs by exploiting the advan- tages of both generational and steady-state algorithms. All the proposed approaches have been extensively examined against existing state-of-the-art methods, showing fairly good performance in a variety of test scenarios. The research work presented in the thesis is the output of initiative and novel attempts to tackle some challenging issues in evolutionary multiobjective optimization. This re- search has not only extended the applicability of some of the existing approaches, such as decomposition-based or Pareto-based algorithms, for complex or hard MOPs, but also contributed to moving forward research in the field of dynamic multiobjective optimiza- tion with novel ideas including new test suites and novel algorithm design

A steady-state and generational evolutionary algorithm for dynamic multi-objective optimization

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods

Development and Integration of Geometric and Optimization Algorithms for Packing and Layout Design

The research work presented in this dissertation focuses on the development and application of optimization and geometric algorithms to packing and layout optimization problems. As part of this research work, a compact packing algorithm, a physically-based shape morphing algorithm, and a general purpose constrained multi-objective optimization algorithm are proposed. The compact packing algorithm is designed to pack three-dimensional free-form objects with full rotational freedom inside an arbitrary enclosure such that the packing efficiency is maximized. The proposed compact packing algorithm can handle objects with holes or cavities and its performance does not degrade significantly with the increase in the complexity of the enclosure or the objects. It outputs the location and orientation of all the objects, the packing sequence, and the packed configuration at the end of the packing operation. An improved layout algorithm that works with arbitrary enclosure geometry is also proposed. Different layout algorithms for the SAE and ISO luggage are proposed that exploit the unique characteristics of the problem under consideration. Several heuristics to improve the performance of the packing algorithm are also proposed. The proposed compact packing algorithm is benchmarked on a wide variety of synthetic and hypothetical problems and is shown to outperform other similar approaches. The physically-based shape morphing algorithm proposed in this dissertation is specifically designed for packing and layout applications, and thus it augments the compact packing algorithm. The proposed shape morphing algorithm is based on a modified mass-spring system which is used to model the morphable object. The shape morphing algorithm mimics a quasi-physical process similar to the inflation/deflation of a balloon filled with air. The morphing algorithm starts with an initial manifold geometry and morphs it to obtain a desired volume such that the obtained geometry does not interfere with the objects surrounding it. Several modifications to the original mass-spring system and to the underlying physics that governs it are proposed to significantly speed-up the shape morphing process. Since the geometry of a morphable object continuously changes during the morphing process, most collision detection algorithms that assume the colliding objects to be rigid cannot be used efficiently. And therefore, a general-purpose surface collision detection algorithm is also proposed that works with deformable objects and does not require any preprocessing. Many industrial design problems such as packing and layout optimization are computationally expensive, and a faster optimization algorithm can reduce the number of iterations (function evaluations) required to find the satisfycing solutions. A new multi-objective optimization algorithm namely Archive-based Micro Genetic Algorithm (AMGA2) is presented in this dissertation. Improved formulation for various operators used by the AMGA2 such as diversity preservation techniques, genetic variation operators, and the selection mechanism are also proposed. The AMGA2 also borrows several concepts from mathematical sciences to improve its performance and benefits from the existing literature in evolutionary optimization. A comprehensive benchmarking and comparison of AMGA2 with other state-of-the-art optimization algorithms on a wide variety of mathematical problems gleaned from literature demonstrates the superior performance of AMGA2. Thus, the research work presented in this dissertation makes contributions to the development and application of optimization and geometric algorithms

Handling Dynamic Multiobjective Optimization Environments via Layered Prediction and Subspace-Based Diversity Maintenance

Peer reviewedPostprin

Dynamic multi-objective optimization: a two archive strategy

Existing studies on dynamic multi-objective optimization mainly focus on dynamic problems with time-dependent objective functions. Few works have put efforts on dynamic problems with a changing number of objectives, or dynamic problems with time-dependent constraints. When problems have time-dependent objective functions, the shape or position of the Pareto-optimal front/set may change over time. However, when dealing with problems with a changing objective number or time-dependent constraints, the challenges are different. Changing number of objectives leads to the expansion or contraction of the dimensions of the Pareto-optimal front/set manifold, while time-dependent constraints may change the shape of feasible regions over time. The existing dynamic handling techniques can hardly handle the changing number of objectives. The state-of-arts in constraints handling techniques are incapable of tackling problems with time-dependent constraints. In this thesis, we present our attempts toward tackling 1) the dynamic multiobjective optimizing problems with a changing number of objectives and 2) multi-objective optimizing problems with time-dependent constraints. Two-archive Evolutionary Algorithms are proposed. Comprehensive experiments are conducted on various benchmark problems for both types of dynamics. Empirical results fully demonstrate the effectiveness of our proposed algorithms