Many real world optimizationproblems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a v...
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Many real world optimizationproblems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search space. Depending on the values of dimensional variables, the number and type of the variables of the problem can vary dynamically. MVOPs and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of scientific challenges in the design of metaheuristics. Standard metaheuristics have been first designed to address continuous or discrete optimizationproblems, and are not able to tackle VMVOPs in an efficient way. The development of metaheuristics for solving such problems has attracted the attention of many researchers and is increasingly popular. However, to our knowledge there is no well established taxonomy or comprehensive survey for handling this important family of optimizationproblems. This paper presents an unified taxonomy for metaheuristic solutions for solving VMVOPs in an attempt to provide a common terminology and classification mechanisms. It provides a general mathematical formulation and concepts of VMVOPs, and identifies the various solving methodologies than can be applied in metaheuristics. The advantages, the weaknesses and the limitations of the presented methodologies are discussed. The proposed taxonomy also allows to identify some open research issues which needs further in-depth investigations.
As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that th...
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As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called EDA(mvn) is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of EDA(mvn) was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, EDA(mvn) outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo.
Modularity, a design philosophy in which a structure is comprised of identical components called modules, offers economical advantages as the modules can be mass produced in high quality controlled facilities. Prior r...
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Modularity, a design philosophy in which a structure is comprised of identical components called modules, offers economical advantages as the modules can be mass produced in high quality controlled facilities. Prior research investigated structural optimization as a means of improving modular design, focusing on optimizing separately (i) the module topology and the module spatial orientation or (ii) the dynamic grouping into families of different topologies. This research did not include stability despite its considerable importance during preliminary design. In this paper, a novel integrated strategy is proposed for the preliminary design of modular trusses, unifying module topology, spatial orientation, and grouping optimization, as well as stability considerations to define meaningful solutions for real-life case studies. This is addressed by formulating an appropriate mixed-variable minimum volume problem in elastic design, including multiple load cases with self-weight and stress limitations in tension and compression. Global stability is considered through a linear prebuckling constraint, and a local buckling constraint is formulated by considering Euler buckling with standard profiles obtained from commercial catalogues. The practical applicability of this contribution is demonstrated on a benchmark modular bridge and a three-dimensional modular vault structure. The importance of stability considerations is also investigated, where the redundancy introduced by modularity is shown to contribute to the global resistance of the entire structure.
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