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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization
Evolutionary multitasking has recently emerged as a novel paradigm that
enables the similarities and/or latent complementarities (if present) between
distinct optimization tasks to be exploited in an autonomous manner simply by
solving them together with a unified solution representation scheme. An
important matter underpinning future algorithmic advancements is to develop a
better understanding of the driving force behind successful multitask
problem-solving. In this regard, two (seemingly disparate) ideas have been put
forward, namely, (a) implicit genetic transfer as the key ingredient
facilitating the exchange of high-quality genetic material across tasks, and
(b) population diversification resulting in effective global search of the
unified search space encompassing all tasks. In this paper, we present some
empirical results that provide a clearer picture of the relationship between
the two aforementioned propositions. For the numerical experiments we make use
of Sudoku puzzles as case studies, mainly because of their feature that
outwardly unlike puzzle statements can often have nearly identical final
solutions. The experiments reveal that while on many occasions genetic transfer
and population diversity may be viewed as two sides of the same coin, the wider
implication of genetic transfer, as shall be shown herein, captures the true
essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure
Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması
Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized
Differential Evolution for Multiobjective Portfolio Optimization
Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution
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