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♮-convexity and its applications in operations

Xin CHEN

《工程管理前沿（英文）》 2017年第4卷第3期页码 283-294 doi: 10.15302/J-FEM-2017057

摘要： -convexity, one of the central concepts in discrete convex analysis, receives significant attentions in the operations literature in recent years as it provides a powerful tool to derive structures of optimal policies and allows for efficient computational procedures. In this paper, we present a survey of key properties of -convexity and some closely related results in lattice programming, several of which were developed recently and motivated by operations applications. As a new contribution to the literature, we establish the relationship between a notion called -differential monotonicity and -convexity. We then illustrate the techniques of applying -convexity through a detailed analysis of a perishable inventory model and a joint inventory and transshipment control model with random capacities.

关键词： L^&natur -convexity lattice programming perishable inventory models random capacity

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The convexity about ultimate bearing hypersurfaces of structures

Chengxi GUO,Tingting GUO

《结构与土木工程前沿（英文）》 2016年第10卷第4期页码 456-461 doi: 10.1007/s11709-016-0334-1

摘要： The relationship between the convexity on the ultimate bearing surface of a structure and the second-order effects of loads is discussed. All of generalized non-overload forces acted on a structure forms a convex set when ignoring the second-order effects (coupling effects between the generalized forces). It is true also when the Hessian matrix composed of the second-order partial derivatives on the hypersurface about the ultimate bearing of the structure is negative definite. The outward convexity is kept when the surface is expressed by certain dimensionless parameters. A series of properties based on the convexity are pointed out. Some applications in the analysis of bearing capacity of structures were illustrated with examples. The study shows that an evaluation about the bearing capacity state of a complex structure can be made on the basis of several points on the surface of the ultimate bearing of the structure.

关键词： service limit load ultimate bearing surface convexity generalized force generalized displacement frame structure

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Application of the invasive weed optimization algorithm to economic dispatch problems

T. JAYABARATHI, Afshin YAZDANI, V. RAMESH

《能源前沿（英文）》 2012年第6卷第3期页码 255-259 doi: 10.1007/s11708-012-0202-1

摘要： In this paper the invasive weed optimization algorithm has been applied to a variety of economic dispatch (ED) problems. The ED problem is concerned with minimizing the fuel cost by optimally loading the electrical generators which are committed to supply a given demand. Some involve prohibited operating zones, transmission losses and valve point loading. In general, they are non-linear non-convex optimization problems which cannot be directly solved by conventional methods. In this work the invasive weed algorithm, a meta-heuristic method inspired by the proliferation of weeds, has been applied to four numerical examples and has resulted in promising solutions compared to published results.

关键词： economic dispatch (ED) invasive weed optimization non-convexity prohibited operating zones (POZ) valve point loading meta-heuristic