A Guaranteed Global Convergence Social Cognitive Optimizer

From the analysis of the traditional social cognitive optimization (SCO) in theory, we see that traditional SCO is not guaranteed to converge to the global optimization solution with probability one. So an improved social cognitive optimizer is proposed, which is guaranteed to converge to the global optimization solution. The global convergence of the improved SCO algorithm is guaranteed by the strategy of periodic restart in use under the conditions of participating in comparison, which helps to avoid the premature convergence. Then we give the convergence proof for the improved SCO based on Solis and Wets’ research results. Finally, simulation results on a set of benchmark problems show that the proposed algorithm has higher optimization efficiency, better global performance, and better stable optimization outcomes than the traditional SCO for nonlinear programming problems (NLPs)

Using Optimality Theory and Reference Points to Improve the Diversity and Convergence of a Fuzzy-Adaptive Multi-Objective Particle Swarm Optimizer

Particle Swarm Optimization (PSO) has received increasing attention from the evolutionary optimization research community in the last twenty years. PSO is a metaheuristic approach based on collective intelligence obtained by emulating the swarming behavior of bees. A number of multi-objective variants of the original PSO algorithm that extend its applicability to optimization problems with conflicting objectives have also been developed; these multi-objective PSO (MOPSO) algorithms demonstrate comparable performance to other state-of-the-art metaheuristics. The existence of multiple optimal solutions (Pareto-optimal set) in optimization problems with conflicting objectives is not the only challenge posed to an optimizer, as the latter needs to be able to identify and preserve a well-distributed set of solutions during the search of the decision variable space. Recent attempts by evolutionary optimization researchers to incorporate mathematical convergence conditions into genetic algorithm optimizers have led to the derivation of a point-wise proximity measure, which is based on the solution of the achievement scalarizing function (ASF) optimization problem with a complementary slackness condition that quantifies the violation of the Karush-Kuhn-Tucker necessary conditions of optimality. In this work, the aforementioned KKT proximity measure is incorporated into the original Adaptive Coevolutionary Multi-Objective Swarm Optimizer (ACMOPSO) in order to monitor the convergence of the sub-swarms towards the Pareto-optimal front and provide feedback to Mamdani-type fuzzy logic controllers (FLCs) that are utilized for online adaptation of the algorithmic parameters. The proposed Fuzzy-Adaptive Multi-Objective Optimization Algorithm with the KKT proximity measure (FAMOPSOkkt) utilizes a set of reference points to cluster the computed nondominated solutions. These clusters interact with their corresponding sub-swarms to provide the swarm leaders and are also utilized to manage the external archive of nondominated solutions. The performance of the proposed algorithm is evaluated on benchmark problems chosen from the multi-objective optimization literature and compared to the performance of state-of-the-art multi-objective optimization algorithms with similar features

Multiobjective differential evolution based on fuzzy performance feedback: Soft constraint handling and its application in antenna designs

The recently emerging Differential Evolution is considered one of the most powerful tools for solving optimization problems. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity, robustness and high speed of convergence. Differential evolution is attractive to researchers all over the world as evidenced by recent publications. There are many variants of differential evolution proposed by researchers and differential evolution algorithms are continuously improved in its performance. Performance of differential evolution algorithms depend on the control parameters setting which are problem dependent and time-consuming task. This study proposed a Fuzzy-based Multiobjective Differential Evolution (FMDE) that exploits three performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. We apply the fuzzy inference rules to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in this algorithm. The proposed FMDE is evaluated on the well known ZDT, DTLZ, and WFG benchmark test suites. The experimental results show that FMDE is competitive with respect to the chosen state-of-the-art multiobjective evolutionary algorithms. The advanced version of FMDE with adaptive crossover rate (AFMDE) is proposed. The proof of concept AFMDE is then applied specifically to the designs of microstrip antenna array. Furthermore, the soft constraint handling technique incorporates with AFMDE is proposed. Soft constraint AFMDE is evaluated on the benchmark constrained problems. AFMDE with soft constraint handling technique is applied to the constrained non-uniform circular antenna array design problem as a case study

Filter-based stochastic algorithm for global optimization

We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.The authors are grateful to the anonymous referees for their fruitful comments and suggestions.The first and second authors were partially supported by Brazilian Funds through CAPES andCNPq by Grants PDSE 99999.009400/2014-01 and 309303/2017-6. The research of the thirdand fourth authors were partially financed by Portuguese Funds through FCT (Fundação para Ciência e Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM and UIDB/00319/2020

Investigating evolutionary computation with smart mutation for three types of Economic Load Dispatch optimisation problem

The Economic Load Dispatch (ELD) problem is an optimisation task concerned with how electricity generating stations can meet their customers’ demands while minimising under/over-generation, and minimising the operational costs of running the generating units. In the conventional or Static Economic Load Dispatch (SELD), an optimal solution is sought in terms of how much power to produce from each of the individual generating units at the power station, while meeting (predicted) customers’ load demands. With the inclusion of a more realistic dynamic view of demand over time and associated constraints, the Dynamic Economic Load Dispatch (DELD) problem is an extension of the SELD, and aims at determining the optimal power generation schedule on a regular basis, revising the power system configuration (subject to constraints) at intervals during the day as demand patterns change. Both the SELD and DELD have been investigated in the recent literature with modern heuristic optimisation approaches providing excellent results in comparison with classical techniques. However, these problems are defined under the assumption of a regulated electricity market, where utilities tend to share their generating resources so as to minimise the total cost of supplying the demanded load. Currently, the electricity distribution scene is progressing towards a restructured, liberalised and competitive market. In this market the utility companies are privatised, and naturally compete with each other to increase their profits, while they also engage in bidding transactions with their customers. This formulation is referred to as: Bid-Based Dynamic Economic Load Dispatch (BBDELD). This thesis proposes a Smart Evolutionary Algorithm (SEA), which combines a standard evolutionary algorithm with a “smart mutation” approach. The so-called ‘smart’ mutation operator focuses mutation on genes contributing most to costs and penalty violations, while obeying operational constraints. We develop specialised versions of SEA for each of the SELD, DELD and BBDELD problems, and show that this approach is superior to previously published approaches in each case. The thesis also applies the approach to a new case study relevant to Nigerian electricity deregulation. Results on this case study indicate that our SEA is able to deal with larger scale energy optimisation tasks

New Strategies for Global Optimization of Chemical Engineering Applications by Differential Evolution

Ph.DDOCTOR OF PHILOSOPH

Hybrid meta-heuristics for combinatorial optimization

Combinatorial optimization problems arise, in many forms, in vari- ous aspects of everyday life. Nowadays, a lot of services are driven by optimization algorithms, enabling us to make the best use of the available resources while guaranteeing a level of service. Ex- amples of such services are public transportation, goods delivery, university time-tabling, and patient scheduling. Thanks also to the open data movement, a lot of usage data about public and private services is accessible today, sometimes in aggregate form, to everyone. Examples of such data are traffic information (Google), bike sharing systems usage (CitiBike NYC), location services, etc. The availability of all this body of data allows us to better understand how people interacts with these services. However, in order for this information to be useful, it is necessary to develop tools to extract knowledge from it and to drive better decisions. In this context, optimization is a powerful tool, which can be used to improve the way the available resources are used, avoid squandering, and improve the sustainability of services. The fields of meta-heuristics, artificial intelligence, and oper- ations research, have been tackling many of these problems for years, without much interaction. However, in the last few years, such communities have started looking at each other’s advance- ments, in order to develop optimization techniques that are faster, more robust, and easier to maintain. This effort gave birth to the fertile field of hybrid meta-heuristics.openDottorato di ricerca in Ingegneria industriale e dell'informazioneopenUrli, Tommas

Analysis and management of security constraints in overstressed power systems

Management of operational security constraints is one of the important tasks performed by system operators, which must be addressed properly for secure and economic operation. Constraint management is becoming an increasingly complex and challenging to execute in modern electricity networks for three main reasons. First, insufficient transmission capacity during peak and emergency conditions, which typically result in numerous constraint violations. Second, reduced fault levels, inertia and damping due to power electronic interfaced demand and stochastic renewable generation, which are making network more vulnerable to even small disturbances. Third, re-regulated electricity markets require the networks to operate much closer to their operational security limits, which typically result in stressed and overstressed operating conditions. Operational security constraints can be divided into static security limits (bus voltage and branch thermal limits) and dynamic security limits (voltage and angle stability limits). Security constraint management, in general, is formulated as a constrained, nonlinear, and nonconvex optimization problem. The problem is usually solved by conventional gradient-based nonlinear programming methods to devise optimal non-emergency or emergency corrective actions utilizing minimal system reserves. When the network is in emergency state with reduced/insufficient control capability, the solution space of the corresponding nonlinear optimization problem may be too small, or even infeasible. In such cases, conventional non-linear programming methods may fail to compute a feasible (corrective) control solution that mitigate all constraint violations or might fail to rationalize a large number of immediate post-contingency constraint violations into a smaller number of critical constraints. Although there exists some work on devising corrective actions for voltage and thermal congestion management, this has mostly focused on the alert state of the operation, not on the overstressed and emergency conditions, where, if appropriate control actions are not taken, network may lose its integrity. As it will be difficult for a system operator to manage a large number of constraint violations (e.g. more than ten) at one time, it is very important to rationalize the violated constraints to a minimum subset of critical constraints and then use information on their type and location to implement the right corrective actions at the right locations, requiring minimal system reserves and switching operations. Hence, network operators and network planners should be equipped with intelligent computational tools to “filter out” the most critical constraints when the feasible solution space is empty and to provide a feasible control solution when the solution space is too narrow. With an aim to address these operational difficulties and challenges, this PhD thesis presents three novel interdependent frameworks: Infeasibility Diagnosis and Resolution Framework (IDRF), Constraint Rationalization Framework (CRF) and Remedial Action Selection and Implementation Framework (RASIF). IDRF presents a metaheuristic methodology to localise and resolve infeasibility in constraint management problem formulations (in specific) and nonlinear optimization problem formulations (in general). CRF extends PIDRF and reduces many immediate post-contingency constraint violations into a small number of critical constraints, according to various operational priorities during overstressed operating conditions. Each operational priority is modelled as a separate objective function and the formulation can be easily extended to include other operational aspects. Based on the developed CRF, RASIF presents a methodology for optimal selection and implementation of the most effective remedial actions utilizing various ancillary services, such as distributed generation control, reactive power compensation, demand side management, load shedding strategies. The target buses for the implementation of the selected remedial actions are identified using bus active and reactive power injection sensitivity factors, corresponding to the overloaded lines and buses with excessive voltage violations (i.e. critical constraints). The RASIF is validated through both static and dynamic simulations to check the satisfiability of dynamic security constraints during the transition and static security constraints after the transition. The obtained results demonstrate that the framework for implementation of remedial actions allows the most secure transition between the pre-contingency and post-contingency stable equilibrium points