Benchmarking Evolutionary Algorithms For Single Objective Real-valued Constrained Optimization - A Critical Review

Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.Comment: This manuscript is a preprint version of an article published in Swarm and Evolutionary Computation, Elsevier, 2018. Number of pages: 4

An efficient constraint handling method for genetic algorithms

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter. Careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region. Once sufficient feasible solutions are found, a niching method (along with a controlled mutation operator) is used to maintain diversity among feasible solutions. This allows a real-parameter GA's crossover operator to continuously find better feasible solutions, gradually leading the search near the true optimum solution. GAs with this constraint handling approach have been tested on nine problems commonly used in the literature, including an engineering design problem. In all cases, the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Genetic Algorithm Design for Constrained Optimization

School of Electrical and Computer Engineerin

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

Partial Evaluation Strategies for Expensive Evolutionary Constrained Optimization

Constrained optimization problems (COPs) are frequently encountered in real-world design applications. For some COPs, the evaluation of the objective(s) and/or constraint(s) may involve significant computational/temporal/financial cost. Such problems are referred to as expensive COPs (ECOPs). Surrogate modeling has been widely used in conjunction with optimization methods for such problems, wherein the search is partially driven by an approximate function instead of true expensive evaluations. However, for any true evaluation, nearly all existing methods compute all objective and constraint values together as one batch. Such full evaluation approaches may be inefficient for cases where the objective/constraint(s) can be evaluated independently of each other. In this article, we propose and study a constraint handling strategy for ECOPs using partial evaluations. The constraints are evaluated in a sequence determined based on their likelihood of being violated; and the evaluation is aborted if a constraint violation is encountered. Modified ranking strategies are introduced to effectively rank the solutions using the limited information thus obtained, while saving on significant function evaluations. The proposed algorithm is compared with a number of its variants to establish the utility of its key components systematically. Numerical experiments and benchmarking are conducted on a range of mathematical and engineering design problems to demonstrate the efficacy of the approach compared to state-of-The-Art evolutionary optimization approaches

River Basin Water Quality Management Models: A State-of-the-Art Review

With the increasing human activities within river basins, the problem of water quality management is becoming increasingly important. Quality management can be achieved through control/prevention measures that have various economic and water quality implications. To facilitate the analysis of available management options, decision models are needed which represent the many facets of the problem. Such models must be capable of adequately depicting the hydrological, chemical and biological processes occurring in the river; while incorporating social, economic and political considerations within the decision framework. Management analyses can be performed using simulation, optimization, or both, depending on the management goal and the size and type of the problem. The critical issues in a management model are the nonlinearities, uncertainties, multiple pollutant nature of waste discharges, multiple objectives, and the spatial and temporal distribution of management actions. Literature on various management models were reviewed under the headings of linear, nonlinear and dynamic programming approaches; their stochastic counterparts, and combined or miscellaneous approaches. Dynamic programming was found to be an attractive methodology which can exploit the sequential decision problem pertaining to river basin water quality problems (downstream control actions do not influence water quality upstream). DP handles discrete decision variables which represent discrete management alternatives, and it is generic in the sense that both linear and non-linear water quality models expressing the relation between emissions and ambient quality levels can be incorporated. An example problem is presented which demonstrates the application of a DP-based management model to formulate least-cost strategies for the Nitra River basin in Slovakia. However, it is hardly possible for a single model to represent all the aspects of a complex decision problem. Different types of management models (e.g. deterministic vs stochastic models) have different capabilities and limitations. The only way to compensate for the deficiencies is to perform the analysis in a sensitivity style. The necessity for sensitivity analyses is further implied due to the fact that water quality problems are rather loosely formulated with respect to the quality and economic goals