Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimization. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimization. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimization, but MOEAs based on non-dominance, such as PMODE, may not

Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework

Simplicity and flexibility of meta-heuristic optimization algorithms have attracted lots of attention in the field of optimization. Different optimization methods, however, hold algorithm-specific strengths and limitations, and selecting the best-performing algorithm for a specific problem is a tedious task. We introduce a new hybrid optimization framework, entitled Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL), which combines the strengths of different evolutionary algorithms (EAs) in a parallel computing scheme. SC-SAHEL explores performance of different EAs, such as the capability to escape local attractions, speed, convergence, etc., during population evolution as each individual EA suits differently to various response surfaces. The SC-SAHEL algorithm is benchmarked over 29 conceptual test functions, and a real-world hydropower reservoir model case study. Results show that the hybrid SC-SAHEL algorithm is rigorous and effective in finding global optimum for a majority of test cases, and that it is computationally efficient in comparison to algorithms with individual EA

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Deadline Constrained Cloud Computing Resources Scheduling through an Ant Colony System Approach

Cloud computing resources scheduling is essential for executing workflows in the cloud platform because it relates to both execution time and execution cost. In this paper, we adopt a model that optimizes the execution cost while meeting deadline constraints. In solving this problem, we propose an Improved Ant Colony System (IACS) approach featuring two novel strategies. Firstly, a dynamic heuristic strategy is used to calculate a heuristic value during an evolutionary process by taking the workflow topological structure into consideration. Secondly, a double search strategy is used to initialize the pheromone and calculate the heuristic value according to the execution time at the beginning and to initialize the pheromone and calculate heuristic value according to the execution cost after a feasible solution is found. Therefore, the proposed IACS is adaptive to the search environment and to different objectives. We have conducted extensive experiments based on workflows with different scales and different cloud resources. We compare the result with a particle swarm optimization (PSO) approach and a dynamic objective genetic algorithm (DOGA) approach. Experimental results show that IACS is able to find better solutions with a lower cost than both PSO and DOGA do on various scheduling scales and deadline conditions