Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm.

Real-world problems often involve the optimisation of multiple conflicting objectives. These problems, referred to as multi-objective optimisation problems, are especially challenging when more than three objectives are considered simultaneously. This paper proposes an algorithm to address this class of problems. The proposed algorithm is an evolutionary algorithm based on an evolution strategy framework, and more specifically, on the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES). A novel selection mechanism is introduced and integrated within the framework. This selection mechanism makes use of an adaptive grid to perform a local approximation of the hypervolume indicator which is then used as a selection criterion. The proposed implementation, named Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (CMA-PAES-HAGA), overcomes the limitation of CMA-PAES in handling more than two objectives and displays a remarkably good performance on a scalable test suite in five, seven, and ten-objective problems. The performance of CMA-PAES-HAGA has been compared with that of a competition winning meta-heuristic, representing the state-of-the-art in this sub-field of multi-objective optimisation. The proposed algorithm has been tested in a seven-objective real-world application, i.e. the design of an aircraft lateral control system. In this optimisation problem, CMA-PAES-HAGA greatly outperformed its competitors

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

An adaptive multi-population differential artificial bee colony algorithm for many-objective service composition in cloud manufacturing

Several conflicting criteria must be optimized simultaneously during the service composition and optimal selection (SCOS) in cloud manufacturing, among which tradeoff optimization regarding the quality of the composite services is a key issue in successful implementation of manufacturing tasks. This study improves the artificial bee colony (ABC) algorithm by introducing a synergetic mechanism for food source perturbation, a new diversity maintenance strategy, and a novel computing resources allocation scheme to handle complicated many-objective SCOS problems. Specifically, differential evolution (DE) operators with distinct search behaviors are integrated into the ABC updating equation to enhance the level of information exchange between the foraging bees, and the control parameters for reproduction operators are adapted independently. Meanwhile, a scalarization based approach with active diversity promotion is used to enhance the selection pressure. In this proposal, multiple size adjustable subpopulations evolve with distinct reproduction operators according to the utility of the generating offspring so that more computational resources will be allocated to the better performing reproduction operators. Experiments for addressing benchmark test instances and SCOS problems indicate that the proposed algorithm has a competitive performance and scalability behavior compared with contesting algorithms

Dynamic Multi-Objectives 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

Preference focussed many-objective evolutionary computation

Solving complex real-world problems often involves the simultaneous optimisation of multiple con icting performance criteria, these real-world problems occur in the elds of engineering, economics, chemistry, manufacturing, physics and many more. The optimisation process usually involves some design challenges in the form of the optimisation of a number of objectives and constraints. There exist many traditional optimisation methods (calculus based, random search, enumerative, etc...), however, these only o er a single solution in either adequate performance in a narrow problem domain or inadequate performance across a broad problem domain. Evolutionary Multi-objective Optimisation (EMO) algorithms are robust optimisers which are suitable for solving complex real-world multi-objective optimisation problems, as they are able to address each of the con icting objectives simultaneously. Typically, these EMO algorithms are run non-interactively with a Decision Maker (DM) setting the initial parameters of the algorithm and then analysing the results at the end of the optimisation process. When EMO is applied to real-world optimisation problems there is often a DM who is only interested in a portion of the Pareto-optimal front, however, incorporation of DM preferences is often neglected in the EMO literature. In this thesis, the incorporation of DM preferences into EMO search methods has been explored. This has been achieved through the review of EMO literature to identify a powerful method of variation, Covariance Matrix Adaptation (CMA), and its computationally infeasible EMO implementation, MO-CMA-ES. A CMA driven EMO algorithm, CMA-PAES, capable of optimisation in the presence of many objectives has been developed, benchmarked, and statistically veri ed to outperform MO-CMA-ES and MOEA/D-DRA on selected test suites. CMA-PAES and MOEA/D-DRA with the incorporation of the novel Weighted Z-score (WZ) preference articulation operator (supporting a priori, a posteriori or progressive incorporation) are then benchmarked on a range of synthetic and real-world problems. WZ-CMA-PAES is then successfully applied to a real-world problem regarding the optimisation of a classi er for concealed weapon detection, outperforming previously published classi er implementations

A Systematic Investigation of Multi-Objective Evolutionary Algorithms Applied to the Water Distribution System Problem

Water distribution systems (WDSs) are one of society’s most important infrastructure assets. They consist of a great number of pumps, valves, junctions and a tremendous number of pipes that connect these nodes within the system, all of which induce a significant capital cost at the time of construction. However, there is no singular option for designing a WDS, and each potential design affects the cost and performance of the system differently (i.e., the pressure at each node and flow rates for each pipe). To identify solutions with a better trade-off between the cost and performance, multi-objective evolutionary algorithms (MOEAs) provide a robust optimisation tool to solve this type of problem. This PhD thesis focuses on improving and developing a more effective MOEA for WDS problems, and optimisation problems in general. The first stage of the research is to study the impact of select critical processes in MOEAs on algorithm performance and understand the reasons behind the performance observations. There are two chapters related to the first stage. The second stage is to develop a proposed General Multi-Objective Evolutionary Algorithm (GMOEA) and compare this with existing MOEAs for WDS problems. This is associated with the third content chapter. In the first paper, the impact of the operators on an algorithm’s performance has been studied. The operators are the key component for exchange of information between solutions in populations to produce offspring solutions, thereby exploring alternative regions of the search space. These have a significant impact on an algorithm’s search behaviour. However, the composition and number of operators that should be included in an MOEA is generally fixed, based on choices made by the developers of these algorithms. To explore this issue, an assessment was conducted via comprehensive numerical experiments that isolate the influence of the size of the operator set, as well as its composition. In addition, the relative influence of other search processes affecting search behaviour (e.g., the selection strategy and hyperheuristic) have been studied. It has been found that operator set size is a dominant factor affecting algorithm performance, having a greater influence than operator set composition and other search processes affecting algorithm search behaviour. Moreover, it was also found that an existing MOEAs’ performance can be improved by simply increasing the number of operators used within the algorithm. This finding can be applied to justify the usage of operators for designing a new MOEA in the future. In the second paper, a new convex hull contribution selection strategy for population-based MOEAs (termed CHCGen) has been proposed and compared with existing MOEAs in order to study the impact of the selection strategy on MOEA performance. It has been found that the CHCGen selection strategy is able to emphasise selection of the population of solutions on the convex hull of the non-dominated set of solutions. The CHCGen selection strategy has demonstrated that it can also improve an existing MOEAs’ performance. The finding suggests different selection strategies have an impact on MOEA performance. In addition, CHCGen can be used for developing a new MOEA in the future. In the third paper, a new multi-objective evolutionary algorithm, called GMOEA(CHCGen,12,T,A)1 has been proposed by conducting comprehensive numerical experiments to determine the optimised component configuration for each MOEA process. The components considered within the algorithm construction include: the selection strategy, hyperheuristic, and operator set size. The numerical experiments not only explore the impact of each process’s component on algorithm performance comprehensively, but also investigate the correlation of each pairwise combination of the process’s components. In addition, the optimal form of the algorithm GMOEA(CHCGen,12,T,A) was compared with seven other existing MOEAs with an extended computational budget for a range of WDS problems. From the results, GMOEA(CHCGen,12,T,A) was shown not only to have outperformed all other MOEAs considered, but also to find a greater number of new Pareto front solutions for intermediate and large scale problems.Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 202