A hybrid of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems

Abstract

The proposed multi-objective optimization algorithm hybridizes random global search with a local refinement algorithm. The global search algorithm mimics the Bayesian multi-objective optimization algorithm. The site of current computation of the objective functions by the proposed algorithm is selected by randomized simulation of the bi-objective selection by the Bayesian-based algorithm. The advantage of the new algorithm is that it avoids the inner complexity of Bayesian algorithms. A version of the Hooke–Jeeves algorithm is adapted for the local refinement of the approximation of the Pareto front. The developed hybrid algorithm is tested under conditions previously applied to test other Bayesian algorithms so that performance could be compared. Other experiments were performed to assess the efficiency of the proposed algorithm under conditions where the previous versions of Bayesian algorithms were not appropriate because of the number of objectives and/or dimensionality of the decision space.

Modified Hooke-Jeeves optimization of operating parameters for required slider speeds and displacements in a feeder slider-crank mechanism

“…It is observed that Hooke-Jeeves method is essentially a direct numerical optimization method, which has been reliably and extensively implemented in many industrial problems such as these [11][12][13][14][15][16][17]19]. Due to the fact that numerical data are available from the numerical solutions of a highly non-linear differential equation, minimization of the errors defined previously requires the use of a commensurate method.…”

“…For instance, Li and Rahman [14] suggested a modification to Hooke-Jeeves optimization method by applying pattern move immediately after a successful pattern move instead of an exploratory move first to maintain the movement in the optimum direction. Litvinas [15] utilized a hybrid optimization of Bayesian-based global search supported with Hooke-Jeeves local search for multi-objective optimization. In that study, the multi-objective problem was reduced to a single objective problem during the application of Hooke-Jeeves method for local refinement process.…”

“…In all these studies on Hooke-Jeeves optimization method [11][12][13][14][15][16][17], it is commonly shared that (i) an increment amount is randomly defined for exploratory search by the user; (ii) a multiplier of one is taken for the pattern move from the base point; (iii) the process is stopped as soon as no move is established by repeatedly dividing the increment amount, which may not make sure that optimization objective is mathematically achieved. However, all these quantities mentioned above are numerically determined here in this work on a mathematical basis such that finally the difference between the actual and desired objects, referred to as the objective function, is practically zero, implying to the achievement of optimum.…”

Performance Analysis and Optimization of Solar-Coupled Mine Water-Source Heat Pump Combined Heating and Cooling System

“…Consequently, it is difficult to achieve global optimization by using a traditional single optimization algorithm. The PSO-HJ hybrid optimization algorithm, which combines the particle swarm optimization algorithm (PSO) and the Hooke-Jeeves algorithm, firstly provides a set of better initial points through the global search ability of the PSO [27], and then further optimizes the system near the initial points found by the PSO through the local search ability of Hooke-Jeeves [28], thereby enhancing the global search and convergence ability and avoiding premature convergence of the optimization.…”