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In this paper we propose a hybrid metaheuristic based on Particle Swarm Optimization, which we tailor on a portfolio selection problem. To motivate and apply our hybrid metaheuristic, we reformulate the portfolio selection problem as an unconstrained problem, by means of penalty functions in the framework of the exact penalty methods. Our metaheuristic is hybrid as it adaptively updates the penalty parameters of the unconstrained model during the optimization process. In addition, it iteratively refines its solutions to reduce possible infeasibilities. We report also a numerical case study. Our hybrid metaheuristic appears to perform better than the corresponding Particle Swarm Optimization solver with constant penalty parameters. It performs similarly to two corresponding Particle Swarm Optimization solvers with penalty parameters respectively determined by a REVAC-based tuning procedure and an irace-based one, but on average it just needs less than 4% of the computational time requested by the latter procedures.

In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.

This study discusses the role of the equivalence factor and penalty function in improving the performance of energy consumption minimization strategies in Range Extended Electric Vehicles (REEVs). In conventional ECMS, equivalence factors are typically derived from constant efficiency assumptions for simplicity or adaptively adjusted according to driving conditions in adaptive ECMS. In REEVs, however, the battery efficiency exhibits nonlinear behavior in the low SOC range, which directly leads to variability in the equivalence factor within conventional ECMS. This study investigates the influence of the variable equivalence factor on the overall fuel economy. The equivalence factors are usually considered constant or vary adaptively depending on driving cycles. However, the variation in battery efficiency is often neglected. The present study compares the results obtained for both constant and variable battery efficiencies in deriving the equivalence factors. The simulation results show that an improvement of approximately 3% in fuel economy was obtained for UDDS, NEDC, and WLTC driving cycles as a result of applying the variable equivalence factor. Additionally, through an analysis of various penalty function designs, the study highlights their crucial role in optimizing fuel consumption across different driving cycles.

Differential search (DS) is a recently developed derivative-free global heuristic optimization algorithm for solving unconstrained optimization problems. In this paper, by applying the idea of exact penalty function approach, a DS algorithm, where an S-type dynamical penalty factor is introduced so as to achieve a better balance between exploration and exploitation, is developed for constrained global optimization problems. To illustrate the applicability and effectiveness of the proposed approach, a comparison study is carried out by applying the proposed algorithm and other widely used evolutionary methods on 24 benchmark problems. The results obtained clearly indicate that the proposed method is more effective and efficient over the other widely used evolutionary methods for most these benchmark problems.

This research proposes a class of filled objective penalty functions for seeking global optimal solutions to minimax constrained optimization problems. A class of objective penalty functions is constructed to obtain the local optimal solutions. Building upon these local optimal solutions, the article introduces a class of objective penalty functions with filled properties, termed as filled penalty functions. Using these filled penalty functions, our algorithm finds a globally approximate solution in finite steps. The time complexity is also analyzed. Finally, straightforward numerical examples are provided to demonstrate the effectiveness of the proposed algorithm.

The derivation of necessary conditions of optimality for optimal control problems with state/control constraints is a challenging task, not always clearly understood. In this paper, we present a didactic approach based on the method of exponential penalty functions allowing, in our setting, to significantly simplify the proofs. This work may be viewed as a proposal of a course designed for students familiar with the basics of optimal control theory and elements of functional analysis. To make the analysis as simple as possible, we concentrate on the case of optimal control problem with fixed initial point and free end state.

In this paper, we use the exact l1 penalty function method to solve a multi-dimensional first-order PDE constrained control optimization problem. The relationships between the aforesaid problem and its associated penalized problem with the exact l1 penalty function are established. Further, we show that an optimal solution to the considered problem is a minimizer of its associated penalized problem under the hypothesis of convex Lagrange functional. In addition, the theoretical results are justified with some examples.

The paper presents an estimation of the optimum cost of an isolated foundation following the safety and serviceability guidelines of Indian Standard (IS) 456:2000. Two adaptable optimization algorithms are developed for the first time to optimize the cost of any type of isolated footing design. Two optimization methods, i.e., constrained binary-coded genetic algorithm, with static penalty function approach and unified particle swarm optimization are developed in MATLAB compliant for optimal design of any isolated foundations. The objective function formulated is based on the total cost of footing. This includes the cost of concrete, the cost of steel and cost of formwork. The design variables which influence the total cost of footing are plan area and depth of footing and area of flexural reinforcement at moment critical sections. The footing design algorithm is developed according to the biaxial-isolated rectangular footing as per IS codes. The constraints, e.g., dimension of footing, restriction on bending, shear stresses and displacements, are considered in the footing design algorithm which acted as a subroutine to the developed optimization programs. Four different numerical examples have been solved to evaluate the versatility of the developed method. A comparison study has been done to observe the efficacy of both the optimization methods.

In this paper we propose an exact, deterministic, and fully continuous reformulation of generalized Nash games characterized by the presence of soft coupling constraints in the form of distributionally robust (DR) joint chance-constraints (CCs). We first rewrite the underlying uncertain game introducing mixed-integer variables to cope with DR–CCs, where the integer restriction actually amounts to a binary decision vector only, and then extend it to an equivalent deterministic problem with one additional agent handling all those introduced variables. Successively we show that, by means of a careful choice of tailored penalty functions, the extended deterministic game with additional agent can be equivalently recast in a fully continuous setting.

In this paper, we propose a method to smooth the general lower-order exact penalty function for inequality constrained optimization. We prove that an approximation global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem. We develop an algorithm based on the smoothed penalty function. It is shown that the algorithm is convergent under some mild conditions. The efficiency of the algorithm is illustrated with some numerical examples.