A Parallel Multi-objective Memetic Algorithm Based on the IGD+ Indicator

In recent years, the use of decomposition methods has become a popular choice to solve complex multi-objective optimization problems. One possible approach to enhance the performance of a decomposition method is to couple it to a local search engine that speeds up convergence to the true Pareto front of a problem. Here, we propose a new local search strategy for continuous search spaces, which is based on the law of reflection of light. Our proposed approach computes reflected rays in order to explore and exploit promising subregions of the search space. The local search engine uses information of the Penalty Boundary Intersection method to create a scene with three elements: 1) a light source defined by the solution which is farthest from the ideal point, 2) a hyperspherical structure built by non-dominated neighboring solutions and 3) a set of reflected rays located in decision variable space. Our proposed local search engine is coupled to MOEA/D (a popular decomposition-based multi-objective optimizer) and is able to outperform three state-of-the-art multi-objective evolutionary algorithms, particularly in multifrontal problems.

An important implementation issue in the design of hybrid evolutionary multiobjective optimization algorithms with local search (i.e., multiobjective memetic algorithms) is how to strike a balance between local search and global search. If local search is applied to all individuals at every generation, almost all computation time is spent by local search. As a result, global search ability of memetic algorithms is not well utilized. We can use three ideas for decreasing the computation load of local search. One idea is to apply local search to only a small number of individuals. This idea can be implemented by introducing a local search probability, which is used to choose only a small number of initial solutions for local search from the current population. Another idea is a periodical (i.e., intermittent) use of local search. This idea can be implemented by introducing a local search interval (e.g., every 10 generations), which is used to specify when local search is applied. The other idea is an early termination of local search. Local search for each initial solution is terminated after a small number of neighbors are examined. This idea can be implemented by introducing a local search length, which is the number of examined neighbors in a series of iterated local search from a single initial solution. In this paper, we discuss the use of these three ideas to strike a local-global search balance. Through computational experiments on a two-objective 500-item knapsack problem, we compare various settings of local search such as short local search from all individuals at every generation, long local search from only a few individuals at every generation, and periodical long local search from all individuals. Global search in this paper means genetic search by crossover and mutation in multiobjective memetic algorithms.

This chapter describes the use of a multiobjective memetic algorithm in aerodynamic shape optimization applications using computational fluid dynamics(CFD). A systematic overviewon multiobjective optimization is given. It covers parameterized scalarization, population-based Pareto front forming using evolutionary algorithms, formulation of Pareto front improvement using local search methods, and various possible heuristics that can be applied in formulating efficient memetic algorithms. A constrained local search, combined with a non-dominated sorting genetic algorithm with niching in both objective and design space is proposed in the paper. Test function results are given and finally the method is used to solve the robust airfoil design problem using a multi-point formulation.

A multiobjective memetic algorithm with particle swarm optimization and Q-learning-based local search for energy-efficient distributed heterogeneous hybrid flow-shop scheduling problem

Purpose — To provide a theoretical background to understand current local search engines as an aspect of specialized search, and understand the data sources and used technologies. Design/methodology/approach — Selected local search engines are examined and compared toward their use of geographic information retrieval (GIR) technologies, data sources, available entity information, processing, and interfaces. An introduction to the field of GIR is given and its use in the selected systems is discussed. Findings — All selected commercial local search engines utilize GIR technology in varying degrees for information preparation and presentation. It is also starting to be used in regular Web search. However, major differences can be found between the different search engines. Research limitations/implications — This study is not exhaustive and only uses informal comparisons without definitive ranking. Due to the unavailability of hard data, informed guesses were made based on available public interfaces and literature. Practical implications — A source of background information for understanding the results of local search engines, their provenance, and their potential. Originality/value — An overview of GIR technology in the context of commercial search engines integrates research efforts and commercial systems and helps to understand both sides better.

This is a survey of Local Search, a general purpose metaheuristic for finding good solutions of combinatorial optimization problems. It is based on building a sequence of (locally optimal) solutions by: (1) perturbing the current solution; (2) applying local search to that modified solution. At a high level, the method is simple, yet it allows for a detailed use of problem-specific properties. After giving a general framework, we cover the uses of Iterated Local Search on a number of well studied problems.

Performing a local search around solutions found by an evolutionary algorithm is a common practice. Local search is well known to significantly improve the solutions, in particular in the case of combinatorial problems. In this paper a new local search procedure is proposed that uses a locally established utopia point. In the tests in which several instances of the Travelling Salesman Problem (TSP) were solved using an evolutionary algorithm the proposed local search procedure outperformed a local search procedure based on Pareto dominance. Because the local search is focused on improving individual solutions and the multiobjective evolutionary algorithm can improve diversity, various strategies of sharing computational resources between the evolutionary algorithm and the local search are used in this paper. The results attained by the tested methods are compared with respect to computation time, which allows a fair comparison between strategies that distribute computational resources between the evolutionary optimization and the local search in various proportions.

This paper presents a multiobjective memetic algorithm based on adaptive local search chains (MMA-ALSC) for vehicle routing problem with time window (VRPTW) which is an important research area in logistics. As shown in most previous studies, VRPTW is essentially a multiobjective optimization problem and can be solved effectively by the multiobjective algorithms with various local search operators. We have observed, however, that the promising solutions obtained during the process of evolution are not fully utilized to guide the search together with different local search operators. This will lead to the discontinuous and insufficient search in the regions showing promise. To alleviate this drawback, MMA-ALSC is proposed and characterized by combining a multi-directional local search strategy (MD-LS) with an enhanced local search chain technique (eLS-Chain). In MMA-ALSC, on the one hand, with MD-LS, different local search operators are designed to perform the search towards multiple directions with distinct problem-specific knowledge of multiobjective VRPTW (MOVRPTW). On the other hand, with eLS-Chain, the promising solutions obtained during the process of evolution are adaptively selected for the subsequent local search operators. In this way, MMA-ALSC can not only effectively explore the search space in multiple directions, but also fully exploit the promising solutions in a chain-based way. Experimental results on two suites of benchmark instances have demonstrated the competitive performance of MMA-ALSC when compared with other representative algorithms.

This paper proposes a new efficient Multi-objective Memetic Algorithm (MOMA) for probabilistic distribution network expansion planning (DNEP). Recently, the deregulated and competitive power market brings about uncertainty, i.e., random output of distributed generation (DG) such as wind and photovoltaic power, load growths, etc. DG plays a key role to smooth distribution network planning. However, system planners are faced with new uncertain environment. This paper makes use of Monte-Carlo simulation to consider these uncertainties efficiently. Furthermore, a new method is proposed for multi-objective DNEP problems with MOMA that combines Multi-objective meta-heuristics with local search to obtain better solution sets. This paper proposes SPEA2 with Random Multi-start Variable neighborhood LS (RMSVLS) to consider the diversity and accuracy of solution sets. The proposed method is successfully applied to a sample system.

This paper proposes a new method for transmission network expansion planning (TNEP) with Multi-objective Memetic Algorithm (MOMA) in consideration of a probabilistic reliability index. Recently, power networks increase the degree of the uncertainties due to the new environment of power network liberations, the emergences of renewable energy, etc. As a result, the importance of improving power supply reliability with probabilistic approaches has been recognized in power system operation and planning. This paper formulates TNEP as a multi-objective optimization problem that optimizes a probabilistic reliability index as well as the construction cost to obtain a set of the Pareto solutions in Monte Carlo Simulation (MCS). This paper proposes a new method for TNEP with MOMA that combines Multi-objective meta-heuristics (MOMH) with Tabu Search (TS) to obtain better solution sets. MOMH is useful for evaluating a set of the Pareto solutions systematically while TS plays a key role to improve the solution quality. The effectiveness of the proposed method is successfully demonstrated in the IEEE 24-bus system.

Orthogonal simulated annealing for multiobjective optimization

Vertical search engines enable users to find information related to a certain topic. A local search engine is a vertical search engine whose topic revolves around a certain geographical area (such as a city, state, country, etc...) In this paper we describe our experiences developing a crawler for a local search engine for the city of Bellingham, Washington, USA. We focus on the tasks of crawling and indexing a large amount of highly relevant Web pages, and then demonstrate ways in which our search engine has the capability to outperform an industrial search engine.

Search engines are web-based systems used for retrieving information from the Internet. They have economic power because of their positioning between information providers and information seekers. Search engines can influence the flow of information – possible business transactions – by the way information is indexed, stored, and portrayed as search results. If a search engine provides good coverage of website content from one group of information providers (grouped by country or language) to the detriment of another group, it will have economic implications for both groups. It is known that certain developed countries and the language(s) of these countries, have better coverage than other developed countries and their languages. This study investigates for the first time the website coverage of a developing country, South Africa, and one of its indigenous languages, Afrikaans. What does the existence of search engine country bias and/or linguistic bias imply for developing countries such as South Africa? South African information providers would have reason for concern if information seekers’ attention were continually routed abroad by biased search engines. South African information seekers would also be done an injustice if they cannot find local web content (or content in their indigenous languages) due to poor search engine coverage. Biased search results guide them away from cheaper, more convenient local information due to poor coverage of local content. Search engines are negatively impacted in turn, when users become tired of the poor local coverage and unwanted international search results and turn to other tools, such as local search engines, for information retrieval. How severe are the effects of search engine bias on developing countries such as South Africa? The body of knowledge discussing search engine bias is very limited, and this study is motivated by stating that, given the possibility of negative economic implications of such bias for developing economies, more research on this topic is justified and urgently needed. The study revealed that Western website content enjoys better coverage than South African website content. After further investigation it was also found that English website content enjoys better coverage than website content in Afrikaans. There is, therefore, a proven search engine bias in favour of Western developed countries and the English language. Website visibility is also studied as a possible cause of search engine bias. It would seem plausible that a relationship may exist between the coverage of websites by search engines and how visible these websites are to a search engine’s crawlers. For the determination of website visibility, the number of in links towards each sample domain was determined. This study shows that the higher visibility of websites from developed countries is a cause of search engine bias in favour of these websites. With website visibility proven as a cause of bias, the study indicates that South Africa, and possibly other developing countries, is lagging far behind in the race to create highly visible websites surrounded by well-covered hyperlink structures – the kind of websites most likely to be covered by search engine crawlers. It is the responsibilty of information providers from developing countries to create more hyperlinks between websites from their countries, as well as creating visible website content in their indigenous languages. Search engine coverage bias has negative economic implications for developing countries such as South Africa. This paper investigates the severity of country related coverage bias against websites from the South African domain(s) and the correlation between website coverage and website visibility. Other possible causes of coverage bias found in literature include indexing algorithms, ranking algorithms and lexicons struggling with non-English content. Information providers’ lack of knowledge about website coverage and search engine tools is discussed as another possible cause of country bias.

Evolutionary multi-objective algorithms (EMOA) using performance indicators for the selection of individuals have turned out to be a successful technique for multi-objective problems. Especially, the selection based on the $\mathcal{S}$-metric, as implemented in the SMS-EMOA, seems to be effective. A special feature of this EMOA is the greedy (μ + 1) selection. Based on a pathological example for a population of size two and a discrete Pareto front it has been proven that a (μ + 1)- (or 1-greedy) EMOA may fail in finding a population maximizing the $\mathcal{S}$-metric. This work investigates the performance of (μ + 1)-EMOA with small fixed-size populations on Pareto fronts of innumerable size. We prove that an optimal distribution of points can always be achieved on linear Pareto fronts. Empirical studies support the conjecture that this also holds for convex and concave Pareto fronts, but not for continuous shapes in general. Furthermore, the pathological example is generalized to a continuous objective space and it is demonstrated that also (μ + k )-EMOA are not able to robustly detect the globally optimal distribution.

Multioperator search strategy for evolutionary multiobjective optimization