Constraint Handling Technique Research Articles

An Evolutionary Constraint-Handling Technique for Parametric Optimization of a Cancer Immunotherapy Model

Recent studies have shown that evolutionary constraint-handling techniques are capable of solving optimization problems with constraints. However, these techniques are often evaluated based on benchmark test functions instead of real-world problems. This paper presents an application of evolutionary constrained parametric optimization for a breast cancer immunotherapy model formulated based on biological principles and limited clinical results. It proposes a new constraint-handling technique that partitions the population into different sections to enhance the evolutionary search diversity. In addition, the upper bound of each section is reduced dynamically to drive the convergence of individuals toward the feasible solution region. Experimental results show the effectiveness and robustness of the proposed constraint-handling approach in solving parametric optimization problems. Moreover, the evolutionary optimized cancer immunotherapy model can be used for prognostic outcomes in clinical trials and the predictability is considered significant for such a parametric optimization approach.

Low-Computation Adaptive Fuzzy Tracking Control of Unknown Nonlinear Systems With Unmatched Disturbances

This paper investigates the tracking control problem for a family of strict-feedback systems with unknown nonlinear functions as well as unmatched disturbances. A low-computation adaptive fuzzy control strategy combined with a constraint-handling technique is proposed to achieve accurate trajectory tracking and boundedness of the closed-loop signals. In contrast to the existing results: first, without the expense of introducing auxiliary filters, iterative calculation of virtual control signal derivatives at each step of the backstepping design that may cause the explosion of complexity issue is obviated; second, the need for disturbance observers and robust compensators to suppress disturbances and approximation errors that require a mass of online learning parameters for estimation is evaded; and third, a small number of closed-loop signals are incorporated into the input space of fuzzy logic systems for approximation. The result from a comparative simulation further illustrates the superiority of the presented approach.

Two-Archive Evolutionary Algorithm for Constrained Multiobjective Optimization

When solving constrained multi-objective optimization problems, an important issue is how to balance convergence, diversity and feasibility simultaneously. To address this issue, this paper proposes a parameter-free constraint handling technique, two-archive evolutionary algorithm, for constrained multi-objective optimization. It maintains two co-evolving populations simultaneously: one, denoted as convergence archive, is the driving force to push the population toward the Pareto front; the other one, denoted as diversity archive, mainly tends to maintain the population diversity. In particular, to complement the behavior of the convergence archive and provide as much diversified information as possible, the diversity archive aims at exploring areas under-exploited by the convergence archive including the infeasible regions. To leverage the complementary effects of both archives, we develop a restricted mating selection mechanism that adaptively chooses appropriate mating parents from them according to their evolution status. Comprehensive experiments on a series of benchmark problems and a real-world case study fully demonstrate the competitiveness of our proposed algorithm, comparing to five state-of-the-art constrained evolutionary multi-objective optimizers.

SRIFA: Stochastic Ranking with Improved-Firefly-Algorithm for Constrained Optimization Engineering Design Problems

Firefly-Algorithm (FA) is an eminent nature-inspired swarm-based technique for solving numerous real world global optimization problems. This paper presents an overview of the constraint handling techniques. It also includes a hybrid algorithm, namely the Stochastic Ranking with Improved Firefly Algorithm (SRIFA) for solving constrained real-world engineering optimization problems. The stochastic ranking approach is broadly used to maintain balance between penalty and fitness functions. FA is extensively used due to its faster convergence than other metaheuristic algorithms. The basic FA is modified by incorporating opposite-based learning and random-scale factor to improve the diversity and performance. Furthermore, SRIFA uses feasibility based rules to maintain balance between penalty and objective functions. SRIFA is experimented to optimize 24 CEC 2006 standard functions and five well-known engineering constrained-optimization design problems from the literature to evaluate and analyze the effectiveness of SRIFA. It can be seen that the overall computational results of SRIFA are better than those of the basic FA. Statistical outcomes of the SRIFA are significantly superior compared to the other evolutionary algorithms and engineering design problems in its performance, quality and efficiency.

Alternative Constraint Handling Technique for Four-Bar Linkage Motion Generation

This paper proposes an extension of a new concept for four-bar path generation and a new penalty constraint handling technique from our previous work to a motion generation problem. The proposed technique could neglect the timing constraint for problems without prescribed timing, which is found to be an efficient technique for a four-bar path generation problem. Later, the remaining constraints are solved with a new constraint handling technique that also gives high performance. The technique is one kind of penalty function techniques. The present work proposes to combine the previous two methods for solving the four-bar motion generation problems. The comparative study, optimisation of motion generation problems with a new and a traditional penalty techniqueare solved by using self-adaptive population size teaching-learning based optimization (SAP-TLBO), is presented. In this study, three new motion generation test problems are used to test the proposed technique. The results show that the new technique gives acceptable results and can be applied with the motion generation problems without prescribed timing.

Development of Diversity-in-Variable-Aware Constraint Handling Technique for Multi-Objective Optimization

Development of Diversity-in-Variable-Aware Constraint Handling Technique for Multi-Objective Optimization

Optimal reactive power dispatch with uncertainties in load demand and renewable energy sources adopting scenario-based approach

Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study.

Optimization of time, cost and surface roughness in grinding process using a robust multi-objective dragonfly algorithm

Grinding is one of the most commonly used operations in the industry. Optimization of the grinding process can significantly improve the product quality and minimize operational costs and production time. Due to nonlinearity and complexity, optimization of the grinding process is one of the most challenging tasks in the field of mechanical engineering. This paper aims to optimize grinding process considering a tri-objective mathematical model to simultaneous optimization of final surface quality, grinding cost and total process time. To obtain non-dominated Pareto optimal solutions, a novel meta-heuristic algorithm named multi-objective dragonfly algorithm is utilized. Besides, an efficient constraint handling technique is implemented to handle complex operational constraints. Furthermore, an experimental case study is solved using the proposed algorithm and the results are compared to NSGA-II in the literature. The results revealed that the proposed algorithm is able to find non-dominated Pareto optimal solutions and make a significant improvement over the existing approaches.

Optimal Synthesis of Four-Bar Linkage Path Generation through Evolutionary Computation with a Novel Constraint Handling Technique.

This paper presents a novel constraint handling technique for optimum path generation of four-bar linkages using evolutionary algorithms (EAs). Usually, the design problem is assigned to minimize the error between desired and obtained coupler curves with penalty constraints. It is found that the currently used constraint handling technique is rather inefficient. In this work, we propose a new technique, termed a path repairing technique, to deal with the constraints for both input crank rotation and Grashof criterion. Three traditional path generation test problems are used to test the proposed technique. Metaheuristic algorithms, namely, artificial bee colony optimization (ABC), adaptive differential evolution with optional external archive (JADE), population-based incremental learning (PBIL), teaching-learning-based optimization (TLBO), real-code ant colony optimization (ACOR), a grey wolf optimizer (GWO), and a sine cosine algorithm (SCA), are applied for finding the optimum solutions. The results show that new technique is a superior constraint handling technique while TLBO is the best method for synthesizing four-bar linkages.

Opposition-based moth flame optimization with Cauchy mutation and evolutionary boundary constraint handling for global optimization

Moth flame optimization (MFO) algorithm proves to be an excellent choice for numerical optimization. However, for some complex objectives, MFO may get trapped in local optima or suffer from premature convergence. In order to overcome these issues, an improved MFO-based algorithm, called opposition-based moth flame optimization with Cauchy mutation and evolutionary boundary constraint handling (OMFO), is presented. The proposed method integrates opposition-based learning (OBL) with Cauchy mutation (CM) and evolution boundary constraint handling (EBCH) technique with MFO to improve its performance. OBL and EBCH improve the convergence of MFO, while CM helps MFO to escape local optima. The effect of each method (OBL, CM, EBCH) on MFO is validated using 18 benchmark functions and two constrained real-world problems. Simulation results indicate that opposition-based MFO integrated with Cauchy mutation and EBCH has the best performance among the MFO variants. The OMFO algorithm is also compared with various algorithms in the literature and provides competitive results in terms of increased exploitation and exploration capability, improved convergence and local optima avoidance.

FSB-EA: Fuzzy search bias guided constraint handling technique for evolutionary algorithm

Constraint handling technique (CHT) is a critical task for the evolutionary algorithms (EAs) on solving the constrained optimization problems (COPs). In the CHTs development, the definition of the search bias in the search process of an EA is one of the important issues. Based on the different search bias definitions, this study divides the CHTs into two categories: deterministic and non-deterministic techniques. The deterministic techniques define the search bias with an artificial rule. These techniques generally perform well for several scenarios. However, they may have poor performance for some others. This is mainly due to the difficulty to establish an accurate mapping between the complex search scenarios and the uncertain search biases. In contrast with the deterministic techniques, the non-deterministic techniques apply stochastic based methods to escape this mapping establishment which will improve the robustness of the algorithm. However, the probability-based blind random selection can affect negatively on the search efficiency of the algorithm. To compensate the deficiencies of these two categories, this paper proposes a fuzzy search bias guided CHT, namely FSB. The search bias in the FSB is guided by a membership function. It is used to meet the fuzzy knowledge that a solution with large constraint violation biases the search toward solutions with smaller constraint violation and a solution with small constraint violation biases the search toward solutions with better objective function value. The experimental results show that FSB is more robust and more efficient than the other compared techniques.

Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy

A multiperiod generation and transmission expansion planning (G&TEP) problem is considered. This model integrates conventional generation with renewable energy sources, assuming a stochastic approach. The proposed approach is based on a centralized planned transmission expansion. Due to the worldwide recent energy guidelines, it is necessary to generate expansion plans adequate to the forecast demand over the next years. Nowadays, in most energy systems, a public entity develops both the short and long of electricity-grid expansion planning. Due to the complexity of the problem, there are different strategies to find expansion plans that satisfy the uncertainty conditions addressed. We proposed to address the G&TEP problem with a pure genetic algorithm approach. Different constraint-handling techniques were applied to deal with two complex case studies presented. Numerical results are shown to compare the strategies used in the test systems, and key factors such as a prior initialization of population and the estimated minimum number of generations are discussed.

Constraint-handling techniques in surrogate-assisted evolutionary optimization. An empirical study

Many real-world constrained numerical optimization problems are defined through expensive models. An alternative to solve them is by using evolutionary algorithms. However, they usually require a considerable number of evaluations to get a competitive solution, and such task needs a high computational effort. This disadvantage can be tackled with surrogate models. In this paper, a study of the relationship between a surrogate model and different constraint-handling techniques is presented. The surrogate model (k nearest neighbors regression, kNN regression) is assembled into differential evolution with combined variants (DECV), named surrogate-assisted DECV (SA-DECV) to approximate the objective function value and the sum of constraint violation. Additionally, four SA-DECV variants with different constraint-handling techniques are assessed. The best variant is compared against two state-of-the-art algorithms. Twenty-four well-known test problems are solved in the experiments. According to the results, the best variant is the one that uses a ranking process as constraint-handling technique. Furthermore, a case of study is included, where a set of engineering optimization problems is solved with the best variant. Finally, the surrogate model is tested in other DE-based algorithms.

E-BRM: A constraint handling technique to solve optimization problems with evolutionary algorithms

This work presents an enhanced technique to handle constraints in optimization problems solved by evolutionary algorithms: the extended balanced ranking method (E-BRM). It comprises a self-adaptive procedure that deals with two ranking lists, for feasible and infeasible solutions, which are merged during the search process according to the amount of feasible and infeasible candidates within the population.The method is designed to work uncoupled from the optimization algorithm, thus being suitable for implementation along with distinct algorithms. Therefore, to evaluate the proposed constraint-handling technique (CHT), and compare its performance with other CHTs that follow the same uncoupled approach, we have implemented them all into a canonical Genetic Algorithm (GA). Several tests were executed over well-known suites of benchmark functions and also engineering problems. The results provided by the different CHTs are compared not only by direct comparisons, but also by nonparametric statistical Sign test, and Wilcoxon Signed-Rank test. Those comparisons indicate that the E-BRM presented an improved overall performance.

CB-ICA: a crossover-based imperialist competitive algorithm for large-scale problems and engineering design optimization

Optimization is increasingly important due to its application in the real-world problems. The imperialist competitive algorithm (ICA) is a successful optimization algorithm in many applications. However, in solving complex problems, especially in high dimensions, ICA easily falls into local optimal and experiences the premature convergence. In this work, a crossover-based imperialist competitive algorithm (CB-ICA) was proposed for solving this problem. The proposed algorithm faces three changes compared to ICA. To increase the exploration ability, the uniform distribution crossover and levy mutation methods were used in assimilation and revolution steps, respectively. Furthermore, the use of uniform crossover in the imperialist improvement step with appropriate data exchange leads to the improvement of convergence speed toward an optimal solution. The results of trials on 10 unconstrained large-scale tests show the advantage of CB-ICA over ICA and also over the related methods in terms of quality of results, convergence speed and reliability. In addition, the proposed method can be used in solving real-world problems with the use of constraint-handling technique. For this reason, CB-ICA has been compared in five engineering design problems with several state-of-the-art algorithms and obtained acceptable results.

Differential evolution with the adaptive penalty method for structural multi-objective optimization

Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance.

An improved teaching-learning-based optimization for constrained evolutionary optimization

When extending a global optimization technique for constrained optimization, we must balance not only diversity and convergence but also constraints and objective function. Based on these two criteria, the famous teaching-learning-based optimization (TLBO) is improved for constrained optimization. To balance diversity and convergence, an efficient subpopulation based teacher phase is designed to enhance diversity, while a ranking-differential-vector-based learner phase is proposed to promote convergence. In addition, how to select the teacher in the teacher phase and how to rank two solutions in the learner phase have a significant impact on the tradeoff between constraints and objective function. To address this issue, a dynamic weighted sum is formulated. Furthermore, a simple yet effective restart strategy is proposed to settle complicated constraints. By adopting the ε constraint-handling technique as the constraint-handling technique, a constrained optimization evolutionary algorithm, i.e., improved TLBO (ITLBO), is proposed. Experiments on a broad range of benchmark test functions reveal that ITLBO shows better or at least competitive performance against other constrained TLBOs and some other constrained optimization evolutionary algorithms.

Pareto-dominance based adaptive multi-objective optimization for hydrothermal coordinated scheduling with environmental emission

Since hydrothermal optimal operation has been a headache in the energy and electricity field due to its coupled and complex non-convex characteristics, this paper proposes an adaptive second mutation based multi-objective differential evolution (ASMMODE) for hydrothermal coordinated scheduling problems, optimal assignments of hydro output and thermal output are taken to reduce thermal cost and environment pollution simultaneously. Firstly, an adaptive second mutation mechanism is proposed to enhance population diversity to avoid premature problem, and entropy density based distribution control strategy is improved to properly control the diversity distribution of obtained Pareto front, which can provide proper candidate optimal scheme for decision-makers. Followed by taking consideration of complex and coupled constraints, coordinated constraint handling technique is proposed to proper handle system load balance, which can coordinate hydro output and thermal output in each time period. Furthermore, those above improvements are testified on benchmark problems and hydrothermal system, according to comparisons and analysis on statistical results, it reveals that the proposed optimization method can be a viable way for solving hydrothermal optimization problems.

Cooperative Differential Evolution Framework for Constrained Multiobjective Optimization.

This paper presents a cooperative differential evolution framework (CCMODE) for constrained multiobjective optimization, and two instantiations of the CCMODE framework are implemented. The proposed framework has (M+1) populations, including M subpopulations for constrained single-objective optimization and an archive population for constrained M -objective optimization. Each subpopulation performs its own constrained single-objective differential evolution to optimize the assigned constrained single-objective optimization problem. For the archive population, the constraint handling techniques (CHTs) are modified for constrained multiobjective optimization. The proposed framework takes the advantage of existing effective constrained single-objective optimization algorithms, and extends them to deal with constrained multiobjective optimization problems. In two instantiations, two CHTs are implemented in CCMODE framework, respectively. Experiment results on several sets of benchmark problems with two, three, and many objectives show that the proposed algorithm is better than existing state-of-the-art constrained multiobjective evolutionary algorithms. The effectiveness of the subpopulations is also discussed.

A Two-stage State Transition Algorithm for Constrained Engineering Optimization Problems

In this study, a state transition algorithm (STA) is investigated into constrained engineering design optimization problems. After an analysis of the advantages and disadvantages of two well-known constraint-handling techniques, penalty function method and feasibility preference method, a two-stage strategy is incorporated into STA, in which, the feasibility preference method is adopted in the early stage of an iteration process whilst it is changed to the penalty function method in the later stage. Then, the proposed STA is used to solve three benchmark problems in engineering design and an optimization problem in power-dispatching control system for the electrochemical process of zinc. The experimental results have shown that the optimal solutions obtained by the proposed method are all superior to those by typical approaches in the literature in terms of both convergency and precision.