On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Solving Economic Dispatch Problem with Valve-Point Effect using a Modified ABC Algorithm

This paper presents a new approach for solving economic dispatch (ED) problem with valve-point effect using a modified artificial bee colony (MABC) algorithm. Artificial bee colony algorithm is a recent population-based optimization method which has been successfully used in many complex problems. This paper proposes a novel best mechanism algorithm based on a modified ABC algorithm, in which a new mutation strategy inspired from the differential evolution (DE) is introduced in order to improve the exploitation process. To demonstrate the effectiveness of the proposed method, the numerical studies have been performed for two different sample systems. The results of the proposed method are compared with other techniques reported in recent literature. The results clearly show that the proposed MABC algorithm outperforms other state-of-the-art algorithms in solving ED problem with the valve-point effect.DOI:http://dx.doi.org/10.11591/ijece.v3i3.251

A Modified ABC Algorithm for Solving Non-Convex Dynamic Economic Dispatch Problems

In this paper, a modified artificial bee colony (MABC) algorithm is presented to solve non-convex dynamic economic dispatch (DED) problems considering valve-point effects, the ramp rate limits and transmission losses. Artificial bee colony algorithm is a recent population-based optimization method which has been successfully used in many complex problems. A new mutation strategy inspired from the differential evolution (DE) is introduced in order to improve the exploitation process. The feasibility of the proposed method is validated on 5 and 10 units test system for a 24 h time interval. The results are compared with the results reported in the literature. It is shown that the optimum results can be obtained more economically and quickly using the proposed method in comparison with the earlier methods

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