Applying Evolutionary Algorithms to Combinatorial Optimization Problems

A new approach is presented to handle constraints optimization using evolutionary algorithms in this paper. First, we present a specific varying fitness function technique, this technique incorporates the problem's constraints into the fitness function in a dynamic way. The resulting varying fitness function facilitates the EA search. On one hand, The new fitness function without any parameters can properly evaluate not only feasible solution, but also infeasible one, on other hand, the information of the best solution in the current population is also concerned in fitness function, which make search more efficient. Meanwhile, a new crossover operator based on simplex crossover operator and a new PSO mutation operator is also proposed, and both the operators utilize the information of good individuals in the current populations so they can produce high quality offspring. Based on these, a new evolutionary algorithm for constrained optimization problems is proposed. The simulations are made on five widely used benchmark problems, and the results indicate the proposed algorithm is effective.

Evolutionary Negative Selection Algorithms (ENSAs) could be regarded as hybrid algorithms of Evolutionary Algorithms (EAs) and Negative Selection Algorithms (NSAs). The average time complexity of ENSAs on combinational optimization problems has never been studied before. In this paper, the average time complexity of ENSAs on one combinational optimization problem is analyzed. The theoretical results demonstrate that, for the Two Max function, the ENSA with an appropriate matching threshold could perform better than the traditional (N+N) EA. Some simulation experiments on the combinational problem are also done, and the experimental results are consistent with theoretical results.

Playing with complexity: From cellular evolutionary algorithms with coalitions to self-organizing maps

Event Takeover Values (ETV) measure the impact of each individual in the population dynamics of evolutionary algorithms (EA). Previous studies argue that ETV distribution of panmictic EAs fit power laws with exponent between 2.2 and 2.5 and that this property is insensitive to fitness landscapes and design choices of the EAs. One exception is cellular EAs, for which there are deviations of the power law for large values. In this paper, ETVs for structured and panmictic EAs with different population size and mutation probability on several fitness landscapes were computed. Although the ETVs distribution of pamictic EAs is heavy-tailed, the log-log plot of the complementary cumulative distributed function shows no linearity. Furthermore, Vuong's tests on the distributions generated by several instances of the problems conclude that power law models cannot be favored over log-normal models. On the other hand, the tests confirm that cEAs impose significant deviations to the distribution tail.

Towards Software Product Lines Optimization Using Evolutionary Algorithms

Job shop scheduling problem (JSSP) is one of the well‐known NP‐hard combinatorial optimization problems (COPs) that aims to optimize the sequential assignment of finite machines to a set of jobs while adhering to specified problem constraints. Conventional solution approaches which include heuristic dispatching rules and evolutionary algorithms has been largely in use to solve JSSPs. Recently, the use of reinforcement learning (RL) has gained popularity for delivering better solution quality for JSSPs. In this research, we propose an end‐to‐end deep reinforcement learning (DRL) based scheduling model for solving the standard JSSP. Our DRL model uses attention‐based encoder of Transformer network to embed the JSSP environment represented as a disjunctive graph. We introduced Gate mechanism to modulate the flow of learnt features by preventing noise features from propagating across the network to enrich the representations of nodes of the disjunctive graph. In addition, we designed a novel Gate‐based graph pooling mechanism that preferentially constructs the graph embedding. A simple multi‐layer perceptron (MLP) based action selection network is used for sequentially generating optimal schedules. The model is trained using proximal policy optimization (PPO) algorithm which is built on actor critic (AC) framework. Experimental results show that our model outperforms existing heuristics and state of the art DRL based baselines on generated instances and well‐known public test benchmarks. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Surrogate models of fitness have been presented as a way of reducing the number of fitness evaluations required by an evolutionary algorithm. This is of particular interest with expensive fitness functions where the cost of building the model is outweighed by the saving of using fewer function evaluations. In this paper we show how a Markov network model can be used as a surrogate fitness function in a genetic algorithm. We demonstrate this applied to a number of well-known benchmark functions and although the results are good in terms of function evaluations the model-building overhead requires a substantially more expensive fitness function to be worthwhile. We move on to describe a fitness function for feature selection in Case-Based Reasoning, which is considerably more expensive than the other benchmark functions we used. We show that for this problem using the surrogate offers a significant decrease in total run time compared to a GA using the true fitness function.

The maximum cut (MAX-CUT) problem is to find a bipartition of the vertices in a given graph such that the number of edges with ends in different sets reaches the largest. Though, several experimental investigations have shown that evolutionary algorithms (EAs) are efficient for this NP-complete problem, there is little theoretical work about EAs on the problem. In this paper, we theoretically investigate the performance of EAs on the MAX-CUT problem. We find that both the (1+1) EA and the (1+1) EA*, two simple EAs, efficiently achieve approximation solutions of (m/2)+(1/4)s(G) and (m/2)+(1/2)(√{8m+1}-1), where m and s(G) are respectively the number of edges and the number of odd degree vertices in the input graph. We also reveal that for a given integer k the (1+1) EA* finds a cut of size at least k in expected runtime O(nm+1/δ(4k)) and a cut of size at least (m/2)+k in expected runtime O(n(2)m+1/δ((64/3)k(2))), where δ is a constant mutation probability and n is the number of vertices in the input graph. Finally, we show that the (1+1) EA and the (1+1) EA* are better than some local search algorithms in one instance, and we also show that these two simple EAs may not be efficient in another instance.

Proceeding of: IEEE Congress on Evolutionary Computation (CEC 2009), May 18-21 (Monday - Thursday), 2009, Trondheim, Norway.

Generating both accurate and diverse recommendations is required for modern recommender systems. Accurate recommendations can well meet the needs of users, while diverse recommendations can bring users novelty, discover the unknown preferences of users, and can also alleviate the long tail problem. However, these two metrics are conflicting and it is very hard to improve both at the same time. Thus, a compromise needs to be made. The easiest way is using hyperparameters to combine different objective functions or the recommendations of different recommendation algorithms, but it is difficult to determine parameters. Another common strategy is applying multi-objective evolutionary algorithm to provide multiple recommendations for each user, but how to choose the final recommendation becomes a new problem. To this end, we propose a two-phase evolutionary algorithm-based recommendation framework, named EARF. In EARF, a novel fitness function is designed, which converts the evaluation of accuracy and diversity into a single objective and automatically trades off these two goals. Based on the property of recommendation problem and fitness function, the genetic representation and operators are redefined. The experiments on real-world rating datasets indicate that the EARF is effective and the proposed evolutionary algorithm can achieve a good balance between accuracy and diversity.

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time.

This study applies a recently developed evolutionary algorithm (EA) called state of matter search (SMS) to minimize the total energy deficit in the Karun4 reservoir, Iran. The operation of the Karun4 reservoir is influenced by several factors, which requires a multiple criteria framework for selecting the most suitable solution EA. Five EAs, in addition to the SMS, were evaluated for the reservoir operation problem on the basis of four performance criteria and the fitness function (FF) value. The priority assessment on the basis of FF value revealed that the SMS outperformed the other EAs in converging to the optimal solution. However, judged by the other four performance criteria, based on weighted aggregates sum product assessment (WASPAS) technique, particle swarm optimization (PSO) proved superior to the other EAs. This paper’s results show that the selection of a solution EA for solving complex reservoir optimization problem requires a multicriteria decision-making process. Multiobjective evo...

This chapter provides an introduction to evolutionary algorithms (EAs) and their applicability to various biological problems. There is a focus on EAs’ use as an optimization technique for fitting parameters to a model. A number of design issues are discussed including the data structure being operated on (chromosome), the construction of robust fitness functions, and intuitive breeding strategies. Two detailed biological examples are given. The first example demonstrates the EA’s ability to optimize parameters of various ion channel conductances in a model neuron by using a fitness function that incorporates the dynamic range of the data. The second example shows how the EA can be used in a hybrid technique with classification algorithms for more accuracy in the classifier, feature pruning, and for obtaining relevant combinations of features. This hybrid technique allows researchers to glean an understanding of important features and relationships embedded in their data that might otherwise remain hidden.

Target shape design optimization by evolving B-splines with cooperative coevolution

Analog CMOS integrated circuits (ICs) designs depend typically on designer knowledge and experience, as such problems are multivariate and multiobjective, presenting many combinations of input variables to be investigated in order to meet the required specifications. Nowadays, the a posteriori approach is widely used to perform the optimization processes of analog CMOS ICs using evolutionary algorithms. However, these techniques are not totally able to explore potential solutions in specific regions of the Pareto front. Designers then have difficulty in choosing the best solution capable of achieving all desired specifications simultaneously among all the ones found. In this context, the a priori approach using fitness functions has become an important alternative method to overcome these issues of the a posteriori methodology. This paper aims to compare different fitness function profiles used in the a priori optimization processes to boost the effectiveness of the search processes in relation to robustness, accuracy, and yield in analog CMOS ICs designs. We show that the Gaussian profile, proposed here, applied to the lower limit, center value, and upper limit fitness functions is able to improve all the a priori optimization evolutionary techniques investigated, including the genetic, imperialist competitive, and shuffled frog leaping algorithms.