ETEA: A euclidean minimum spanning tree-Based evolutionary algorithm for multiobjective optimization

© the Massachusetts Institute of TechnologyAbstract The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in the space, where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based Evolutionary Algorithm (ETEA) to solve multiobjective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically in ETEA, four strategies are introduced: 1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; 2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; 3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; 4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/K001310/1, and the National Natural Science Foundation of China under Grant 61070088

Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.Comment: 11 pages, 2 tables; v3: minor revisions, to appear in Journal of Global Optimizatio

Multiobjective optimization of electromagnetic structures based on self-organizing migration

Práce se zabývá popisem nového stochastického vícekriteriálního optimalizačního algoritmu MOSOMA (Multiobjective Self-Organizing Migrating Algorithm). Je zde ukázáno, že algoritmus je schopen řešit nejrůznější typy optimalizačních úloh (s jakýmkoli počtem kritérií, s i bez omezujících podmínek, se spojitým i diskrétním stavovým prostorem). Výsledky algoritmu jsou srovnány s dalšími běžně používanými metodami pro vícekriteriální optimalizaci na velké sadě testovacích úloh. Uvedli jsme novou techniku pro výpočet metriky rozprostření (spread) založené na hledání minimální kostry grafu (Minimum Spanning Tree) pro problémy mající více než dvě kritéria. Doporučené hodnoty pro parametry řídící běh algoritmu byly určeny na základě výsledků jejich citlivostní analýzy. Algoritmus MOSOMA je dále úspěšně použit pro řešení různých návrhových úloh z oblasti elektromagnetismu (návrh Yagi-Uda antény a dielektrických filtrů, adaptivní řízení vyzařovaného svazku v časové oblasti…).This thesis describes a novel stochastic multi-objective optimization algorithm called MOSOMA (Multi-Objective Self-Organizing Migrating Algorithm). It is shown that MOSOMA is able to solve various types of multi-objective optimization problems (with any number of objectives, unconstrained or constrained problems, with continuous or discrete decision space). The efficiency of MOSOMA is compared with other commonly used optimization techniques on a large suite of test problems. The new procedure based on finding of minimum spanning tree for computing the spread metric for problems with more than two objectives is proposed. Recommended values of parameters controlling the run of MOSOMA are derived according to their sensitivity analysis. The ability of MOSOMA to solve real-life problems from electromagnetics is shown in a few examples (Yagi-Uda and dielectric filters design, adaptive beam forming in time domain…).