Non-dominated sorting genetic algorithm with decomposition to solve constrained optimisation problems

Cooperative perception constitutes a critical technology to enhance situational awareness of vehicular users (VUs) by fusing multi-source observation data. Existing approaches employ either vehicles or road infrastructure as fusion platforms. However, vehicle-based approaches suffer from severe occlusions that compromise perception reliability, while infrastructure-based approaches are constrained by fixed coverage ranges that restrict spatial perception, thereby failing to achieve both reliable and comprehensive perception simultaneously. To overcome these limitations, we propose an uncrewed aerial vehicle (UAV)-enabled cooperative perception system where a UAV operates in a cyclic process: it adjusts its position to respond to VU requests, collects observation data, and returns the compressed fusion results to the VUs. In each cycle, we jointly optimize decisions regarding UAV trajectory, request response, data collection, compression degree of the fusion results, and resource allocation to balance fusion reliability and service latency, subject to UAV kinematics, task assignment, resource allocation, and latency constraints. We formulate this optimization problem as a dynamic constrained multi-objective optimization problem featuring cascaded dependencies where the request response, data collection, and resource allocation should be determined sequentially due to the inherent logic of cooperative perception. To solve this problem, we design an evolutionary algorithm based on a cascaded dependency generation strategy in which decision variables are generated according to their dependency order. Experimental results demonstrate the superior solution performance of our algorithm over four baseline algorithms. This study advances cooperative perception for vehicular networks by providing a UAV-enabled solution ensuring reliable fusion and timely service under dynamic traffic conditions.

Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

In parallel to optimizing energy consumption within houses, users' comfort is increasingly considered as an essential success criterion for automated smart home solutions. From the user perspective, balancing trade-offs between energy consumption and users' comfort when scheduling home appliances is a challenging task mainly within dynamic context (energy price, budget, user preferences, energy source, etc). To address this challenge, this paper has modeled appliances scheduling as a dynamic constrained multi-objective optimization problem and have leveraged a recently introduced dynamic evolutionary algorithm for the problem resolution. Moreover, there are typically multiple inhabitants in the same home who often share context-aware applications with various individual preferences which are likely to be conflicting. We propose a new comfort function to support multi-user conflictual preferences. Our experimental results have shown that our approach has a confirmed advantage on the user comfort while coping dynamically with the context changes.

We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.

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

An empirical study of the algorithm dynamic differential evolution with combined variants with a repair method (DDECV $$+$$+ Repair) in the solution of dynamic constrained optimization problems is presented. Unexplored aspects of the algorithm are of particular interest in this work: (1) the role of each one of its elements, (2) its sensitivity to different change frequencies and change severities in the objective function and the constraints, (3) its ability to detect a change and recover after it, besides its diversity handling (percentage of feasible and infeasible solutions) during the search, and (4) its performance with dynamism present in different parts of the problem. Seven performance measures, eighteen recently proposed test problems and eight algorithms found in the specialized literature are considered in four experiments. The statistically validated results indicate that DDECV $$+$$+ Repair is robust to change frequency and severity variations, and that it is particularly fast to recover after a change in the environment, but highly depends on its repair method and its memory population to provide competitive results. DDECV $$+$$+ Repair shows evidence on the convenience of keeping a proportion of infeasible solutions in the population when solving dynamic constrained optimization problems. Finally, DDECV $$+$$+ Repair is highly competitive particularly when dynamism is present in both, objective function and constraints.

A proposal for a memory design is given that is suitable for solving constrained dynamic optimization problems by an evolutionary algorithm. Based on ideas from abstract memory, two schemes, blending and censoring, are introduced and tested. Using a new benchmark we show in numerical experiments that such a memory can improve solving certain types of constrained dynamic problems.

In this paper, a convex filled function method for solving constrained global optimization problems is proposed. A convex filled function is proposed by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a convex filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems.

In this paper, energy efficient power control for small cells underlaying a macro cellular network is investigated. We formulate the power control problem in self-organizing small cell networks as a non-cooperative game, and propose a distributed energy efficient power control scheme, which allows the small base stations (SBSs) to take individual decisions for attaining the Nash equilibrium (NE) with minimum information exchange. Specially, in the non-cooperative power control game, a non-convex optimization problem is formulated for each SBS to maximize their energy efficiency (EE). By exploiting the properties of parameter-free fractional programming and the concept of perspective function, the non-convex optimization problem for each SBS is transformed into an equivalent constrained convex optimization problem. Then, the constrained convex optimization problem is converted into an unconstrained convex optimization problem by exploiting the mixed penalty function method. The inequality constraints are eliminated by introducing the logarithmic barrier functions and the equality constraint is eliminated by introducing the quadratic penalty function. We also theoretically show the existence and the uniqueness of the NE in the non-cooperative power control game. Simulation results show remarkable improvements in terms of EE by using the proposed scheme.

In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.

Chapter five - Multivariable constrained nonlinear optimization

This work presents a stochastic global optimization (SGO) approach, which integrates an artificial immune algorithm and a particle swarm optimization (AIA-PSO) approach. to solve constrained engineering design optimization problems (e.g., tension/compression string design and pressure vessel design problems), the proposed AIA-PSO algorithm uses a penalty function method to transform a constrained engineering design optimization problem to an unconstrained optimization problem. Based on an external AIA approach, the constriction coefficient, cognitive parameter, social parameter, penalty parameter and mutation probability of an internal PSO algorithm are optimized. Constrained engineering design optimization problems are then solved using the internal PSO algorithm. Moreover, numerical results obtained using the proposed AIA-PSO algorithm is compared with those of published individual genetic algorithm (GA) with AIA methods and hybrid algorithms. Experimental results indicate that the optimum parameter settings of the internal PSO algorithm can be obtained using the external AIA approach. Also, the proposed AIA-PSO algorithm performs significantly better than those of some published individual GA with AIA approaches and hybrid algorithms for solving the pressure vessel design problem. Therefore, the proposed AIA-PSO algorithm can be considered as a promising SGO approach for solving constrained engineering design optimization problems.

In this paper, a modified version of spider monkey optimization (SMO) algorithm for solving constrained optimization problems has been proposed. To the best of author's knowledge, this is the first attempt to develop a version of SMO which can solve constrained continuous optimization problems by using the Deb's technique for handling constraints. The proposed algorithm is named constrained spider monkey optimization (CSMO) algorithm. The performance of CSMO is investigated on the well-defined constrained optimization problems of CEC2006 and CEC2010 benchmark sets. The results of the proposed algorithm are compared with constrained versions of particle swarm optimization, artificial bee colony and differential evolution. Outcome of the experiment and the discussion of results demonstrate that CSMO handles the global optimization task very well for constrained optimization problems and shows better performance in comparison with compared algorithms. Such an outcome will be an encouragement for the research community to further explore the potential of SMO in solving benchmarks as well as real-world problems, which are often constrained in nature.

In this paper, we formulate human motion tracking as a high dimensional constrained dynamic optimization problem. A novel generative method, called Sequential Immune Genetic Algorithm, is proposed for human motion tracking. The main contribution is that we introduce immune genetic algorithm (IGA) for pose optimization in latent space of human motion. As the latent space is low-dimensional and contains the prior knowledge of human motion, it makes pose analysis more efficient and accurate. We apply IGA for pose optimization. Compared with GA and other evolutionary methods, its main advantage is the ability to use the prior knowledge of human motion. As motion tracking is a dynamic optimization problem, we incorporate the temporal continuity information into the traditional IGA and propose a sequential IGA (S-IGA) algorithm. We demonstrate our methods on different videos of different motion types. Experimental results show that the S-IGA motion tracking method can achieve accurate and stable tracking of 3D human motion.