English

This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.

A biased random-key genetic algorithm (BRKGA) is a general search procedure for finding optimal or near-optimal solutions to hard combinatorial optimization problems. It is derived from the random-key genetic algorithm of Bean (1994), differing in the way solutions are combined to produce offspring. BRKGAs have three key features that specialize genetic algorithms: A fixed chromosome encoding using a vector of N random keys or alleles over the real interval [0, 1), where the value of N depends on the instance of the optimization problem; A well-defined evolutionary process adopting parameterized uniform crossover to generate offspring and thus evolve the population; The introduction of new chromosomes called mutants in place of the mutation operator usually found in evolutionary algorithms. Such features simplify and standardize the procedure with a set of self-contained tasks from which only one is problem-dependent: that of decoding a chromosome, i.e. using, the keys to construct a solution to the underlying optimization problem, from which the objective function value or fitness can be computed. BRKGAs have the additional characteristic that, under a weak assumption, crossover always produces feasible offspring and, therefore, a repair or healing procedure to recover feasibility is not required in a BRKGA. In this tutorial we review the basic components of a BRKGA and introduce an Application Programming Interface (API) for quick implementations of BRKGA heuristics. We then apply the framework to a number of hard combinatorial optimization problems, including 2-D and 3-D packing problems, network design problems, routing problems, scheduling problems, and data mining. We conclude with a brief review of other domains where BRKGA heuristics have been applied.

This paper describes libbrkga, a GNU-style dynamic shared Python/C++ library of the biased random-key genetic algorithm (BRKGA) for bound constrained global optimization. BRKGA (J Heuristics 17:487---525, 2011b) is a general search metaheuristic for finding optimal or near-optimal solutions to hard optimization problems. It is derived from the random-key genetic algorithm of Bean (ORSA J Comput 6:154---160, 1994), differing in the way solutions are combined to produce offspring. After a brief introduction to the BRKGA, including a description of the local search procedure used in its decoder, we show how to download, install, configure, and use the library through an illustrative example.

The two-dimensional cutting problem has a direct relationship with industry problems. There are several proposals to solve these problems. In particular, solution proposals using metaheuristics are the focus of this research. Thus, in this paper, we present a specialized biased random key genetic algorithm. Several tests were performed using known instances in the specific literature, and the results found by the metaheuristics proposed were, in many cases, equal or superior to the results already published in the literature. Another comparison of results presented in this paper is related to the results obtained by specialized metaheuristics and the results found by a mathematical model using commercial software. Once again, in this case, the genetic algorithm presented results equal to or very close to the optimum found by the mathematical model. In addition, the optimization proposal was extended to two-dimensional non-guillotine cutting without parts orientation.

Optimizing Automated Manufacturing Processes Using a Hybrid BRKGA Algorithm: A Case Study on Flexible Job-Shop Scheduling

This paper combines the chemical reaction optimisation algorithm with the greedy algorithm to solve the three-dimensional bin packing problem (3D-BPP). Traditionally, the 3D-BPP is solved with algorithms based on particle swarm optimisation, genetic algorithm, or simulated annealing algorithm, etc. The chemical reaction optimisation algorithm is proposed in recent years, which has the advantages of traditional simulated annealing algorithm and has a faster convergence speed. After making appropriate adjustments to the chemical reaction optimisation algorithm, the experiment was performed on classic 320 examples. The results show that the proposed algorithm outperforms the existing algorithms such as greedy variable neighbourhood descent (GVND) and biased random key genetic algorithm (BRKGA).

The parallel batch processing machine scheduling problem with two-dimensional bin packing constraints (PBS-2D) has appeared in many industrial environments, but the research on this problem is still not sufficient. In this article, we use the 2-D rectangular packing constraints to describe the spatial geometric layout of jobs more accurately, and propose a mixed integer linear programming (MILP) model to minimize the makespan of PBS-2D. According to the in-depth analysis of the problem properties, PBS-2D is separated into three subproblems, which are job-machine assignment, 2-D job placement, and job sequence optimization. An improved biased random key genetic algorithm (OBRKGA) is proposed to solve job-machine assignment and job sequence optimization. This algorithm generates the initial population based on the idea of orthogonal experimental design, so that the whole solution space can be scanned evenly when generating the initial solution, making the algorithm be more likely to find better solutions for subsequent evolution. At the same time, a bin packing algorithm based on best fit is designed to handle 2-D job placement problem. Finally, the algorithms are tested on a large number of randomly generated instances, the results show that OBRKGA outperformed the original BRKGA, the classical moth-flame optimization algorithm, particle swarm optimization algorithm, gravity search algorithm, and MILP.

Guest Editorial: Situational awareness of integrated energy systems

Obtaining the Grundy chromatic number: How bad can my greedy heuristic coloring be?

This chapter first presents job shop scheduling problems (JSSP) with fuzzy processing time and fuzzy trapezoid or doublet due-date. An efficient random key genetic algorithm (RKGA) is suggested, in which a random key representation and a new decoding strategy are proposed and two-point or discrete crossover are used. Performance analyses on random key representation are done and RKGA is compared with other algorithm. Computations results validate the effectiveness of random key representation and the promising advantage of RKGA on fuzzy scheduling.

Fuzzy job shop scheduling problem with availability constraints

Unit commitment is a key issue in power system operation and has long been an intractable problem due to its complex mix-integer nonlinear formulation. The original unit commitment problem aims to minimize the fossil fuel cost by determining the on/off status of power units and power contribution of each online unit at the same time. However, the uncoordinated large charging power necessity of plug-in electric vehicles brings unprecedented challenges to the power system operators and further complicates the unit commitment problem. To seamless integrate the plug-in electric vehicles into the unit commitment, a new binary/real-value hybrid meta-heuristic algorithm framework is proposed in this paper, simultaneously determining the binary status and power output of units as well as the power delivered to/feedback from flexible charging and discharging of plug-in electric vehicles. A batch of binary particle swarm optimisation variants with different transfer functions are implemented and compared in solving the unit commitment problem with and without plug-in electric vehicles. Numerical studies illustrate the effectiveness of the proposed intelligent algorithm and the impact of different transfer functions is evaluated.

Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

The unit commitment operation in power systems is a complex, non-linear, constrained optimization problem. The commitment and de-commitment decision presents a binary problem which needs discrete/binary optimization approaches. This paper presents a binary bat search algorithm (BBSA) to solve unit commitment (UC) problem. The bat search algorithm belongs to a meta heuristic class of optimization approaches inspired by natural echolocation behavior of bats. In order to solve binary UC problem, the real valued bat search process is mapped to binary search space using sigmoidal transformation function. The BBSA is then applied to test system with 10 thermal units. The effectiveness of the BBSA is verified against system dimension using test systems upto 100 units. Extensive numerical experiments are performed to test the effectiveness of BBSA and statistical analysis of simulation results are presented. The simulation results are presented, discussed and compared to various existing classical and heuristic approaches. The same demonstrate the superior performance of BBSA approach in solving UC problem.