Composite Differential Evolution for Constrained Evolutionary Optimization

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the ϵ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods

Optimal Biocompatible Solvent Design by Mixed-integer Hybrid Differential Evolution

In this study, a flexible optimization approach is introduced to design an optimal biocompatible solvent for an extractive fermentation process with cell-recycling. The optimal process/solvent design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objectives and the constraints. A flexible or fuzzy optimization approach is applied to soften the rigid requirement for maximization of the production rate, extraction efficiency and to consider the solvent utilization rate as the softened inequality constraint to the process/solvent design problem. Such a trade-off problem is then converted to the goal attainment problem, which is described as the constrained mixed-integer nonlinear programming (MINLP) problem. Mixed-integer hybrid differential evolution with multiplier updating method is introduced to solve the constrained MINLP problem. The adaptive penalty updating scheme is more efficient to achieve a global design

The MOEADr Package – A Component-Based Framework for Multiobjective Evolutionary Algorithms Based on Decomposition

Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) represent a widely used class of population-based metaheuristics for the solution of multicriteria optimization problems. We introduce the MOEADr package, which offers many of these variants as instantiations of a component-oriented framework. This approach contributes for easier reproducibility of existing MOEA/D variants from the literature, as well as for faster development and testing of new composite algorithms. The package offers an standardized, modular implementation of MOEA/D based on this framework, which was designed aiming at providing researchers and practitioners with a standard way to discuss and express MOEA/D variants. In this paper we introduce the design principles behind the MOEADr package, as well as its current components. Three case studies are provided to illustrate the main aspects of the package

Fuzzy Differential Evolution Algorithm

The Differential Evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm does not adequately capture vague preliminary knowledge from the problem domain. This thesis proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information of the search space can be represented and used to deliver a more efficient search. The proposed FDE algorithm utilizes fuzzy set theory concepts to modify the traditional DE algorithm search initialization and mutation components. FDE, alongside other key DE features, is implemented in a convenient decision support system software package. Four benchmark functions are used to demonstrate performance of the new FDE and its practical utility. Additionally, the application of the algorithm is illustrated through a water management case study problem. The new algorithm shows faster convergence for most of the benchmark functions

Economic and environmental impacts of the energy source for the utility production system in the HDA process

The well-known benchmark process for hydrodealkylation of toluene (HDA) to produce benzene is revisited in a multi-objective approach for identifying environmentally friendly and cost-effective operation solutions. The paper begins with the presentation of the numerical tools used in this work, i.e., a multi-objective genetic algorithm and a Multiple Choice Decision Making procedure. Then, two studies related to the energy source involved in the utility production system (UPS), either fuel oil or natural gas, of the HDA process are carried out. In each case, a multi-objective optimization problem based on the minimization of the total annual cost of the process and of five environmental burdens, that are Global Warming Potential, Acidification Potential, Photochemical Ozone Creation Potential, Human Toxicity Potential and Eutrophication Potential, is solved and the best solution is identified by use of Multiple Choice Decision Making procedures. An assessment of the respective contribution of the HDA process and the UPS towards environmental impacts on the one hand, and of the environmental impacts generated by the main equipment items of the HDA process on the other hand is then performed to compare both solutions. This ‘‘gate-to-gate’’ environmental study is then enlarged by implementing a ‘‘cradle-togate’’ Life Cycle Assessment (LCA), for accounting of emission inventory and extraction. The use of a natural gas turbine, less economically efficient, turns out to be a more attractive alternative to meet the societal expectations concerning environment preservation and sustainable development

Adaptive multimodal continuous ant colony optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima