Multiobjective optimization with ϵ-constrained method for solving real-parameter constrained optimization problems

Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness

In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same α-pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided.

Controller optimization using data-driven constrained bat algorithm with gradient-based depth-first search strategy

The meta-heuristic algorithms have aroused great attention for controller optimization. However, most of them are inseparable from the explicit system models when addressing a constrained optimization problem (COP). In this paper, we propose a data-driven constrained bat algorithm via a gradient-based depth-first search (GDFS) strategy. In the proposed scheme, the GDFS strategy can predetermine a search space that satisfies some strict constraints (e.g., stability requirements) of the optimized system. Meanwhile, an improved boundary constraint handling method is proposed to limit the exploration process to the predetermined space. In this way, the proposed algorithm can solve the COP by utilizing experimental data from real scenes, thereby relieving the dependence on precisely modeling the complex system. Together with an ɛ-constraint-handling method, the bat algorithm is employed to seek the global optimum of the COP. The search performance is enhanced by the designed linear-varying elite layer-based local search and a social learning-based walk mechanism to dynamically balance exploration and exploitation. The convergence is ensured based on the criteria of the stochastic optimization algorithm. Experimental results on a servo drive system and benchmark test functions verify the effectiveness of the proposed algorithm.

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Numerous multiobjective evolutionary algorithms (EAs) have been designed for constrained optimization over the past two decades. The idea behind these algorithms is to transform constrained optimization problems (COPs) into multiobjective optimization problems without any constraint, and then solve them. In this article, we propose a new multiobjective method for constrained optimization, which works by converting a COP into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that of the constrained problem but a helper objective does not. Then, this multiobjective optimization problem is decomposed into a group of subproblems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyze the computational time of the helper and equivalent objective method on a hard problem called "wide gap." In a wide gap problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the wide gap. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. The experimental results show that its overall performance is ranked first when compared with other eight state-of-the-art EAs on IEEE CEC2017 benchmarks in constrained optimization.