A Multi-state Gravitational Search Algorithm for Combinatorial Optimization Problems

We consider in this paper the adaptation of heuristics used for programming nondeterministic games to the problems of discrete optimization. In particular, we use some “game” heuristic methods of decision-making in various discrete optimization problems. The object of each of these problems is programming anytime algorithms. Among the problems described in this paper, there are the classical traveling salesman problem and some connected problems of minimization for nondeterministic finite automata. The first of the considered methods is the geometrical approach to some discrete optimization problems. For this approach, we define some special characteristics relating to some initial particular case of considered discrete optimization problem. For instance, one of such statistical characteristics for the traveling salesman problem is a significant development of the so-called “distance functions” up to the geometric variant such problem. And using this distance, we choose the corresponding specific algorithms for solving the problem. Besides, other considered methods for solving these problems are constructed on the basis of special combination of some heuristics, which belong to some different areas of the theory of artificial intelligence. More precisely, we shall use some modifications of unfinished branchand-bound method; for the selecting immediate step using some heuristics, we apply dynamic risk functions; simultaneously for the selection of coefficients of the averaging-out, we also use genetic algorithms; and the reductive self-learning by the same genetic methods is also used for the start of unfinished branch-and-bound method again. This combination of heuristics represents a special approach to construction of anytime-algorithms for the discrete optimization problems. This approach can be considered as an alternative to application of methods of linear programming, and to methods of multi-agent optimization, and also to neural networks.

Introducing clustering based population in Binary Gravitational Search Algorithm for Feature Selection

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

The fault diagnosis method of bearing based on lifting wavelet transform (LWT)‐self‐adaptive phase space reconstruction (SPSR)‐singular value decomposition (SVD)‐based relevance vector machine (RVM) with binary gravitational search algorithm (BGSA) is presented in this study, among which LWT‐SPSR‐SVD (LSS) is presented for feature extraction of the bearing vibration signal, the dynamic characteristics of lifting wavelet coefficients′ (LWCs′) reconstructed signals of the bearing vibration signal can be reflected by SPSR for LWCs′ reconstructed signals of the bearing vibration signal, and BGSA is used to select the embedding space dimension and time delay of phase space reconstruction (PSR) and kernel parameter of RVM. In order to show the superiority of LWT‐SPSR‐SVD‐based RVM with BGSA (LSS‐BGSA‐RVM), the traditional RVM trained by the training samples with the features based on LWT‐SVD (LS‐RVM) is used to compare with the proposed LSS‐BGSA‐RVM method. The experimental result demonstrates that compared with LS‐RVM, LSS‐BGSA‐RVM can achieve the higher diagnosis accuracy for bearing.

<p indent="0mm">As a high-performance general-purpose form of parallel solvers, parallel algorithm portfolios (PAPs) have recently shown great performance for solving decision, counting, continuous, and discrete optimization problems. However, the manual construction of PAPs is laborious work, which typically requires substantial domain knowledge and human effort. To address this issue, this paper proposes AutoPAP, an evolutionary intelligence-based method for PAP construction. Overall, AutoPAP follows the (<italic>n</italic>+1) evolutionary framework, i.e., in each generation, <italic>n</italic> candidate algorithms are generated, and the best one among them is retained in the PAP. Considering that the algorithm configuration space is typically very large, this study designs a highly effective mutation operator to improve the practical performance of AutoPAP and further theoretically proves that AutoPAP can achieve (1−1/<italic>e</italic>) approximation. Finally, to validate the effectiveness of AutoPAP, this study uses it to build a PAP, namely, TSP_PAP, for traveling salesman problems (TSPs). The test results show that TSP_PAP significantly outperforms state-of-the-art TSP solvers EAX and LKH in terms of efficiency (runtime) and effectiveness (solution quality). On 128 TSP instances of sizes ranging from 1000 to 30000, compared with LKH and EAX, TSP_PAP can reduce the average runtime by at least 45.71% and lower the average deviation ratio by at least 87.50%, indicating the huge potential of AutoPAP in automatic algorithm design and evolution.

In view of Traveling Salesman Problem (TSP) is a NP hard problem, Lion Swarm Optimization (LSO) Algorithm is a new swarm intelligence optimization algorithm. Therefore, in this paper, it uses improved hybrid LSO algorithm to solve TSP. Because the basic LSO algorithm is mainly used to solve the continuous problem, and the TSP is a discrete combinatorial optimization problem, this paper improves the LSO algorithm, introduces the greedy strategy, and combines with the Population Competitive Search (PCS) algorithm in the later stage of the search. As a result, the convergence speed is accelerated and the search efficiency is improved. The classic TSP example is tested, and the simulation results show that the algorithm proposed in this paper has strong stability and is an effective method for solving TSP.

Discrete tree seed algorithm for urban land readjustment

Most discrete optimization problems belong to the NP-complete or NP-hard classes. A benchmark problem to assess the performance of new heuristics to solve these classes of problems is the traveling salesman problem (TSP). This paper proposes some modifications on a self-organizing network, named RABNET- TSP, to solve TSP problems. The modified algorithm is compared, with encouraging results, to other proposals from the literature on a number of different TSP instances.

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allotment of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which include limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus distribution network and the results are compared with conventional binary particle swarm optimization.

Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search

This paper is concerned with the discrete combinatorial optimization problem. A novel set-based differential evolution (SBDE) algorithm for traveling salesman problem (TSP) is proposed and evaluated. SBDE is based on a set-based representation scheme that enables SBDE to characterize the discrete search space of TSP. The candidate solution, vector and the arithmetical operator in SBDE are redefined. Numerical experiments are carried out using the TSPLIB of test TSP problems. The obtained results show that the proposed approach is effective in quality for solving TSP.

The Traveling Salesman Problem (TSP) is a classical discrete combinatorial optimization problem that is widely applied in various domains, including robotics, transportation, networking, etc. Although existing studies have provided extensive discussions of the TSP, the issues of improving convergence and optimization capability are still open. In this study, we aim to address this issue by proposing a new algorithm named IDINFO (Improved version of the discretized INFO). The proposed IDINFO is an extension of the INFO (weighted mean of vectors) algorithm in discrete space with optimized searching strategies. It applies the multi-strategy search and a threshold-based 2-opt and 3-opt local search to improve the local searching ability and avoid the issue of local optima of the discretized INFO. We use the TSPLIB library to estimate the performance of the IDINFO for the TSP. Our algorithm outperforms the existing representative algorithms (e.g., PSM, GWO, DSMO, DJAYA, AGA, CNO_PSO, Neural-3-OPT, and LIH) when tested against multiple benchmark sets. Its effectiveness was also verified in the real world in solving the TSP in short-distance delivery.

Black hole algorithm (BHA) is a popular metaheuristic algorithm proposed and applied for data clustering in 2013. BHA was applied to continuous and discrete problems; it is also hybridized with some algorithms in the literature. The pure BHA shows better performance than others in discrete optimization, such as traveling salesman problems. However, it requires improving the algorithm with competitive heuristics. Many heuristics have often been used to construct the initial tour of a salesman, such as the nearest neighbor algorithm (NN), nearest insertion algorithm (NI), cheapest insertion algorithm (CI), random insertion algorithm (RI), furthest insertion algorithm (FI), and minimal spanning tree algorithm (MST). In addition, the black hole algorithm is combined with popular heuristics, such as swap/or insert, reverse/or 2-opt swap, and swap-reverse/or 3-opt swap, and tested with proper parameters in this study. In the experimentation, classical datasets are used via TSP-library. The experimental results are given as best, average solutions/or deviations, and CPU time for all datasets. Besides, the hybrid algorithms demonstrate a better performance rate to get optimality. Finally, hybrid algorithms solve the discrete optimization problem in a short computing time for all datasets.

Population-based approaches have given us new search strategies and ideas in order to solve optimization problems. Usually, these methods are based on the performance carried out by a finite number of agents, which by the interaction between them they evolve and work all over the search space. Also, it is well-known that the correct employment of parameter values in this kind of method can positively impact their performance and behavior. In this context, the present work focuses on the design of a hybrid architecture which smartly balances the population size on run-time. In order to smartly balance and control the population size, a modular approach, named Linear Modular Population Balancer (LMPB), is proposed. The main ideas behind the designed architecture include the solving strategy behind a population-based metaheuristic, the influence of learning components based on multiple statistical modeling methods which transform the dynamic data generated into knowledge, and the possibilities to tackle both discrete and continuous optimization problems. In this regard, three modules are proposed for LMPB, which concern tasks such as the management of the population-based algorithm, parameter setting, probabilities, learning methods, and selection mechanism for the population size to employ. In order to test the viability and effectiveness of our proposed approach, we solve a set of well-known benchmark functions and the multidimensional knapsack problem (MKP). Additionally, we illustrate promising solving results, compare them against state-of-the-art methods which have proved to be good options for solving optimization problems, and give solid arguments for future work in the necessity to keep evolving this type of proposed architecture.

In this paper, we propose a framework for employing opposition-based learning to assist evolutionary algorithms in solving discrete and combinatorial optimization problems. To our knowledge, this is the first attempt to apply opposition to combinatorics. We introduce two different methods of opposition to solve two different type of combinatorial optimization problems. The first technique, open-path opposition, is suited for combinatorial problems where the final node in the graph does not have be connected to the first node, such as the graph coloring problem. The latter technique, circular opposition, can be employed for problems where the endpoints of a graph are linked, such as the well-known traveling salesman problem (TSP). Both discrete opposition methods have been hybridized with biogeography-based optimization (BBO). Simulations on TSP benchmarks illustrate that incorporating opposition into BBO improves its performance.