Deep‐Mining Backtracking Search Optimization Algorithm Guided by Collective Wisdom

Abstract

The backtracking search optimization algorithm (BSA) is a recently proposed evolutionary algorithm with simple structure and well global exploration capability, which has been widely used to solve optimization problems. However, the exploitation capability of the BSA is poor. This paper proposes a deep-mining backtracking search optimization algorithm guided by collective wisdom (MBSAgC) to improve its performance. The proposed algorithm develops two learning mechanisms, i.e., a novel topological opposition-based learning operator and a linear combination strategy, by deeply mining the winner-tendency of collective wisdom. The topological opposition-based learning operator guides MBSAgC to search the vertices in a hypercube about the best individual. The linear combination strategy contains a difference vector guiding individuals learning from the best individual. In addition, in order to balance the overall performance, MBSAgC simulates the clusterity-tendency strategy of collective wisdom to develop another difference vector in the above linear combination strategy. The vector guides individuals to learn from the mean value of the current generation. The performance of MBSAgC is tested on CEC2005 benchmark functions (including 10-dimension and 30-dimension), CEC2014 benchmark functions, and a test suite composed of five engineering design problems. The experimental results of MBSAgC are very competitive compared with those of the original BSA and state-of-the-art algorithms.

Optimal allocation of photovoltaic generations in buildings‐to‐distribution‐network integration system using improved backtracking search optimization algorithm

“…Then, based on TOBL, the historical population is updated in terms of the distance of the best fitness population and the current population. Therefore, Equation (A3) in APPENDIX A.2 is adjusted as [37] $$$$\begin{equation} {\hat{F}}^{\rm old-pop}_{i,j}={\left\lbrace \begin{aligned} &F^{\mathrm{opp-pop}}_{i,j}, \quad {\rm if}\ \big\vert \big\vert F^{\mathrm{opt-pop}}_{j}-F^{\mathrm{pop}}_{i,j}\big\vert \big\vert <\big\vert \big\vert F^{\mathrm{opt-pop}}_{j}\\ &-F^{\mathrm{pop}}_{i,j}\big\vert \big\vert F^{\rm pop}_{i,j},\ \ \ \ \ \quad {\rm otherwise} \end{aligned}\right.} \end{equation}$$$$where $$F^{\mathrm{opt-pop}}_{j}$$ is the best population at the j th dimension.…”

A Hybrid Algorithm Framework with Learning and Complementary Fusion Features for Whale Optimization Algorithm

“…e initial lp value is 0.5 and needs to be updated after each iteration. In this paper, lp is designed to control the execution frequency of the search operators in equations (22) and (23) and those in equations (24) and (25). In the process of algorithm evolution, when lp is less than a random number, operator 1 and operator 2 are used to mutate; otherwise, operator 3 and operator 4 are selected to mutate.…”

“…e description of these problems including three-bar truss, pressure vessel, speed reducer, gear train, cantilever beam, and I-beam is given in Appendix A. Table 6 shows the parameter settings of six engineering problems according reference [23,24], where N, T, and D represent the population size, the maximum number of iterations, and the dimension of optimization problems, respectively. However, there are a number of complex constraints in each problem, which make it challenging to find the optimal solution satisfying all the constraints.…”

“…. , X N (5) end (6) end (7) finess � ObjFun(P)% Calculate the fitness of each search agent (8) X * � the best search agent (9) Leaderminimum � the fitness of the best search agent (10) t � 1 and lp � 0.5 (11) while t ≤ T max do (12) Mutation (13) %% Update the Position of search agents (14) for i � 1 to N do (15) Update a, A, C and l (16) if lp < rand then (17) if |A| < 1 then (18) the individual is mutated by equation 22) (19else (20) Select a random individual X rand ; the individual is mutated by equation 23) (21end (22) else (23) if |A| < 1 then (24) the individual is mutated by equation 24) (25else (26) the individual is mutated by equation 25) (27end (28) end (29) end (30) %% Checking allowable range (31) for i � 1 to N do (32) for j � 1 to D do (33) if x ij < lx j or x ij > ux j then (34) x ij � lx j + rand * ux j (35) end (36) end (37) end (38) %% Update the leader (39) for i � 1 to N do (40) fitness(i) � ObjFun(X i )% Calculate objective function values of T (41) if fitness(i) < Leaderminimum then (42) Leaderminimum Scientific Programming e results of WOA-DE and WOA-BSA are compared with WOA, dynamic stochastic selection (DEDS) [27], hybrid evolutionary algorithm (HEAA) [28], hybrid particle swarm optimization with differential evolution (PSO-DE) [29], differential evolution with level comparison (DELC) [30], mine blast algorithm (MBA) [31], and crow search algor...…”

Grey Prediction Evolution Algorithm Based on Accelerated Even Grey Model

“…The G-PEAe is a population-based stochastic search method, which predicts the evolutionary direction at the macroscopic level to lead the population gradually move toward the global optimum. The main difference between GPEAe and other evolutionary algorithms (EAs) [7]- [11] is that GPEAe adopts the prediction theory to obtain the offsprings. Unlike traditional optimization techniques, GPEAe does not rely on gradient information and has the ability in jumping out of local optima.…”