Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently reoptimize linear functions under a dynamic uniform constraint. Motivated by this study, we investigate single- and multi-objective baseline evolutionary algorithms for the classical knapsack problem where the capacity of the knapsack varies over time.
We establish different benchmark scenarios where the capacity changes every $τ$ iterations according to a uniform or normal distribution. Our experimental investigations analyze the behavior of our algorithms in terms of the magnitude of changes determined by parameters of the chosen distribution, the frequency determined by $τ$, and the class of knapsack instance under consideration. Our results show that the multi-objective approaches using a population that caters for dynamic changes have a clear advantage on many benchmarks scenarios when the frequency of changes is not too high. Furthermore, we demonstrate that the diversity mechanisms used in popular evolutionary multi-objective algorithms such as NSGA-II and SPEA2 do not necessarily result in better performance and even lead to inferior results compared to our simple multi-objective approaches.
Evolutionary algorithms are well suited for solving the knapsack problem. Some empirical studies claim that evolutionary algorithms can produce good solutions to the 0-1 knapsack problem. Nonetheless, few rigorous investigations address the quality of solutions that evolutionary algorithms may produce for the knapsack problem. The current paper focuses on a theoretical investigation of three types of (N+1) evolutionary algorithms that exploit bitwise mutation, truncation selection, plus different repair methods for the 0-1 knapsack problem. It assesses the solution quality in terms of the appr…
Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation evolutionary algorithm for solving the 0-1 knapsack problem. Two initialisation methods are considered in the algorithm: local search initialisation and greedy search initialisation. Then the solution quality of the algorithm is analysed in terms of the approximation ratio.
The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of $α$. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knap…
Evolutionary algorithms have been applied to a wide range of stochastic problems. Motivated by real-world problems where constraint violations have disruptive effects, this paper considers the chance-constrained knapsack problem (CCKP) which is a variance of the binary knapsack problem. The problem aims to maximize the profit of selected items under a constraint that the knapsack capacity bound is violated with a small probability. To tackle the chance constraint, we introduce how to construct surrogate functions by applying well-known deviation inequalities such as Chebyshev's inequality and …
Evolutionary multi-objective algorithms have been widely shown to be successful when utilized for a variety of stochastic combinatorial optimization problems. Chance constrained optimization plays an important role in complex real-world scenarios, as it allows decision makers to take into account the uncertainty of the environment. We consider a version of the knapsack problem with stochastic profits to guarantee a certain level of confidence in the profit of the solutions. We introduce the multi-objective formulations of the profit chance constrained knapsack problem and design three bi-objec…
Evolutionary algorithms have been widely used for a range of stochastic optimization problems in order to address complex real-world optimization problems. We consider the knapsack problem where the profits involve uncertainties. Such a stochastic setting reflects important real-world scenarios where the profit that can be realized is uncertain. We introduce different ways of dealing with stochastic profits based on tail inequalities such as Chebyshev's inequality and Hoeffding bounds that allow to limit the impact of uncertainties. We examine simple evolutionary algorithms and the use of heav…
Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize the total profit subject to the probability that total weight exceeds the capacity. We make use of prominent tail inequalities such as Chebyshev's inequality, and Chernoff bound to approximate the probabilistic constrai…
A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.
In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem (KP). Our goal is to evolve a population of solutions that all have a profit of at least $(1-\varepsilon)\cdot OPT$, where OPT is the value of an optimal solution. Furthermore, they should differ in structure with respect to an entropy-based diversity measure. To this end we propose a simple $(μ+1)$-EA with initial approximate solutions calculated by a well-k…
Multi-Objective Evolutionary Optimization of Chance-Constrained Multiple-Choice Knapsack Problems with Implicit Probability Distributions
Southern University of Science and Technology（南方科技大学）；Central China Normal University（华中师范大学）；Institute of High Performance Computing, Agency for Science Technology and Research（新加坡科技研究局高性能计算研究所）；Nanyang Technological University（南洋理工大学）
Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many real-life constrained combinatorial optimization problems which operate on binary space. On the other hand, the quantum inspired evolutionary algorithm (QEA) is very well suitable for handling such problems by applying several quantum computing techniques such as Q-bit representation and rotation gate operator, etc. This paper extends the concept of differential op…
Genetic Algorithm is an evolutionary algorithm and a metaheuristic that was introduced to overcome the failure of gradient based method in solving the optimization and search problems. The purpose of this paper is to evaluate the impact on the convergence of Genetic Algorithm vis-a-vis 0/1 knapsack. By keeping the number of generations and the initial population fixed, different crossover methods like one point crossover and two-point crossover were evaluated and juxtaposed with each other. In addition to this, the impact of different selection methods like rank-selection, roulette wheel and t…
In this paper, we propose a parallel multiobjective evolutionary algorithm called Parallel Criterion-based Partitioning MOEA (PCPMOEA), with an application to the Mutliobjective Knapsack Problem (MOKP). The suggested search strategy is based on a periodic partitioning of potentially efficient solutions, which are distributed to multiple multiobjective evolutionary algorithms (MOEAs). Each MOEA is dedicated to a sole objective, in which it combines both criterion-based and dominance-based approaches. The suggested algorithm addresses two main sub-objectives: minimizing the distance between the …
Addressing a complex real-world optimization problem is a challenging task. The chance-constrained knapsack problem with correlated uniform weights plays an important role in the case where dependent stochastic components are considered. We perform runtime analysis of a randomized search algorithm (RSA) and a basic evolutionary algorithm (EA) for the chance-constrained knapsack problem with correlated uniform weights. We prove bounds for both algorithms for producing a feasible solution. Furthermore, we investigate the behavior of the algorithms and carry out analyses on two settings: uniform …
Multi-objective orienteering problems (MO-OPs) are classical multi-objective routing problems and have received a lot of attention in the past decades. This study seeks to solve MO-OPs through a problem-decomposition framework, that is, a MO-OP is decomposed into a multi-objective knapsack problem (MOKP) and a travelling salesman problem (TSP). The MOKP and TSP are then solved by a multi-objective evolutionary algorithm (MOEA) and a deep reinforcement learning (DRL) method, respectively. While the MOEA module is for selecting cities, the DRL module is for planning a Hamiltonian path for these …
This paper proposes a generalized Hybrid Real-coded Quantum Evolutionary Algorithm (HRCQEA) for optimizing complex functions as well as combinatorial optimization. The main idea of HRCQEA is to devise a new technique for mutation and crossover operators. Using the evolutionary equation of PSO a Single-Multiple gene Mutation (SMM) is designed and the concept of Arithmetic Crossover (AC) is used in the new Crossover operator. In HRCQEA, each triploid chromosome represents a particle and the position of the particle is updated using SMM and Quantum Rotation Gate (QRG), which can make the balance …
This paper extends the analogies employed in the development of quantum-inspired evolutionary algorithms by proposing quantum-inspired Hadamard walks, called QHW. A novel quantum-inspired evolutionary algorithm, called HQEA, for solving combinatorial optimization problems, is also proposed. The novelty of HQEA lies in it's incorporation of QHW Remote Search and QHW Local Search - the quantum equivalents of classical mutation and local search, that this paper defines. The intuitive reasoning behind this approach, and the exploration-exploitation balance thus occurring is explained. From the res…
Estimate Hitting Time by Hitting Probability for Elitist Evolutionary Algorithms
Nottingham Trent University（诺丁汉特伦特大学）；Southern University of Science and Technology（南方科技大学）；University of Nottingham Ningbo China（诺丁汉大学宁波校区）；Lingnan University（岭南大学）
The performance of base-line Evolutionary Algorithms (EAs) on combinatorial problems has been studied rigorously. From the theoretical viewpoint, the literature extensively investigates the linear problems, while the theoretical analysis of the non-linear problems is still far behind. In this paper, variations of the Packing While Travelling (PWT) -- also known as the non-linear knapsack problem -- are studied as an attempt to analyse the behaviour of EAs on non-linear problems from theoretical perspective. We investigate PWT for two cities and $n$ items with correlated weights and profits, us…
Bacteria have been a source of inspiration for the design of evolutionary algorithms. At the beginning of the 20th century synthetic biology was born, a discipline whose goal is the design of biological systems that do not exist in nature, for example, programmable synthetic bacteria. In this paper, we introduce as a novelty the designing of evolutionary algorithms where all the steps are conducted by synthetic bacteria. To this end, we designed a genetic algorithm, which we have named BAGA, illustrating its utility solving simple instances of optimization problems such as function optimizatio…
In more recent years, there has been increasing research interest in exploiting the use of application specific hardware for solving optimisation problems. Examples of solvers that use specialised hardware are IBM's Quantum System One and D-wave's Quantum Annealer (QA) and Fujitsu's Digital Annealer (DA). These solvers have been developed to optimise problems faster than traditional meta-heuristics implemented on general purpose machines. Previous research has shown that these solvers (can optimise many problems much quicker than exact solvers such as GUROBI and CPLEX. Such conclusions have no…
Many kinds of Evolutionary Algorithms (EAs) have been described in the literature since the last 30 years. However, though most of them share a common structure, no existing software package allows the user to actually shift from one model to another by simply changing a few parameters, e.g. in a single window of a Graphical User Interface. This paper presents GUIDE, a Graphical User Interface for DREAM Experiments that, among other user-friendly features, unifies all kinds of EAs into a single panel, as far as evolution parameters are concerned. Such a window can be used either to ask for one…
Continuous Goal-Directed Actions (CGDA) is a robot imitation framework that encodes actions as the changes they produce on the environment. While it presents numerous advantages with respect to other robot imitation frameworks in terms of generalization and portability, final robot joint trajectories for the execution of actions are not necessarily encoded within the model. This is studied as an optimization problem, and the solution is computed through evolutionary algorithms in simulated environments. Evolutionary algorithms require a large number of evaluations, which had made the use of th…
The performance of a Multiobjective Evolutionary Algorithm (MOEA) is crucially dependent on the parameter setting of the operators. The most desired control of such parameters presents the characteristic of adaptiveness, i.e., the capacity of changing the value of the parameter, in distinct stages of the evolutionary process, using feedbacks from the search for determining the direction and/or magnitude of changing. Given the great popularity of the algorithm NSGA-II, the objective of this research is to create adaptive controls for each parameter existing in this MOEA. With these controls, we…
Existing studies on dynamic multi-objective optimization focus on problems with time-dependent objective functions, while the ones with a changing number of objectives have rarely been considered in the literature. Instead of changing the shape or position of the Pareto-optimal front/set when having time-dependent objective functions, increasing or decreasing the number of objectives usually leads to the expansion or contraction of the dimension of the Pareto-optimal front/set manifold. Unfortunately, most existing dynamic handling techniques can hardly be adapted to this type of dynamics. In …
Complutense University of Madrid（马德里康普顿斯大学）；University of Nottingham（诺丁汉大学）
We propose a variation of the standard genetic algorithm that incorporates social interaction between the individuals in the population. Our goal is to understand the evolutionary role of social systems and its possible application as a non-genetic new step in evolutionary algorithms. In biological populations, ie animals, even human beings and microorganisms, social interactions often affect the fitness of individuals. It is conceivable that the perturbation of the fitness via social interactions is an evolutionary strategy to avoid trapping into local optimum, thus avoiding a fast convergenc…
We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state EAs. For the standard bimodal benchmark function \twomax we rigorously prove that using uniform parent selection leads to exponential runtimes with high probability to locate both optima for the standard ($μ$+1)~EA and ($μ$+1)~RLS with any polynomial population sizes. On the other hand, we prove that selecting the worst individual as parent leads to efficient global optimisation with overwhelming probability for reasonable population sizes. Since always selecting the worst individual may ha…
Beijing University of Aeronautics and Astronautics（北京航空航天大学）
Evolutionary algorithms are wildly used in unmanned aerial vehicle path planning for their flexibility and effectiveness. Nevertheless, they are so sensitive to the change of environment that can't adapt to all scenarios. Due to this drawback, the previously successful planner frequently fail in a new scene. In this paper, a first-of-its-kind machine learning method named Evolutionary Programmer is proposed to solve this problem. Concretely, the most commonly used Evolutionary Algorithms are decomposed into a series of operators, which constitute the operator library of the system. The new met…
In this paper, we introduce a new evolutionary optimization algorithm based on Tukey's symmetric lambda distribution. Tukey distribution is defined by 3 parameters, the shape parameter, the scale parameter, and the location parameter or average value. Various other distributions can be approximated by changing the shape parameter, and as a result can encompass a large class of probability distributions. In addition, Because of these attributes, an Evolutionary Programming (EP) algorithm with Tukey mutation operator may perform well in a large class of optimization problems. Various schemes in …
Semantics-Guided Automatic Tensorization for Multiobjective Evolutionary Algorithms: A Multi-Agent Framework
The Hong Kong Polytechnic University（香港理工大学）；The Hong Kong Polytechnic University Shenzhen Research Institute（香港理工大学深圳研究院）；The Hong Kong Polytechnic University-Daya Bay Technology and Innovation Research Institute（香港理工大学-大亚湾技术与创新研究院）
In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The traveling thief problem~(TTP) belongs to this category and is formed by the integration of the traveling salesperson problem~(TSP) and the knapsack problem~(KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity~(QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quali…
University of Southampton（南安普顿大学）；The Alan Turing Institute（阿兰·图灵研究所）
Evolutionary Computation is a group of biologically inspired algorithms used to solve complex optimisation problems. It can be split into Evolutionary Algorithms, which take inspiration from genetic inheritance, and Swarm Intelligence algorithms, that take inspiration from cultural inheritance. However, recent developments have focused on computational or mathematical adaptions, leaving their biological roots behind. This has left much of the modern evolutionary literature relatively unexplored. To understand which evolutionary mechanisms have been considered, and which have been overlooked, t…
University of Southampton（南安普顿大学）；National Oceanography Centre（国家海洋学中心）；The Alan Turing Institute（艾伦·图灵研究所）
Hundreds of Evolutionary Computation approaches have been reported. From an evolutionary perspective they focus on two fundamental mechanisms: cultural inheritance in Swarm Intelligence and genetic inheritance in Evolutionary Algorithms. Contemporary evolutionary biology looks beyond genetic inheritance, proposing a so-called ``Extended Evolutionary Synthesis''. Many concepts from the Extended Evolutionary Synthesis have been left out of Evolutionary Computation as interest has moved toward specific implementations of the same general mechanisms. One such concept is epigenetic inheritance, whi…
Learning classifier systems (LCSs) are evolutionary machine learning algorithms, flexible enough to be applied to reinforcement, supervised and unsupervised learning problems with good performance. Recently, self organizing classifiers were proposed which are similar to LCSs but have the advantage that in its structured population no balance between niching and fitness pressure is necessary. However, more tests and analysis are required to verify its benefits. Here, a variation of the first algorithm is proposed which uses a parameterless self organizing map (SOM). This algorithm is applied in…
In addition to their undisputed success in solving classical optimization problems, neuroevolutionary and population-based algorithms have become an alternative to standard reinforcement learning methods. However, evolutionary methods often lack the sample efficiency of standard value-based methods that leverage gathered state and value experience. If reinforcement learning for real-world problems with significant resource cost is considered, sample efficiency is essential. The enhancement of evolutionary algorithms with experience exploiting methods is thus desired and promises valuable insig…
Online Regime-aware Calibration for Black-box Social Simulators via Posterior-assisted Evolutionary Dynamic Optimization
Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen 518055, China（脑启发智能计算广东省重点实验室，南方科技大学，深圳518055，中国）；Department of Computer Science and Engineering（计算机科学与工程系）；Department of Statistics and Data Science（统计与数据科学系）；Zhongguancun Academy, Beijing 100094, China（中关村学院，北京100094，中国）；School of Data Science, Lingnan University, Hong Kong SAR, China（数据科学学院，岭南大学，香港特别行政区，中国）
Robotics at Google（谷歌机器人团队）；Columbia University（哥伦比亚大学）
Learning adaptable policies is crucial for robots to operate autonomously in our complex and quickly changing world. In this work, we present a new meta-learning method that allows robots to quickly adapt to changes in dynamics. In contrast to gradient-based meta-learning algorithms that rely on second-order gradient estimation, we introduce a more noise-tolerant Batch Hill-Climbing adaptation operator and combine it with meta-learning based on evolutionary strategies. Our method significantly improves adaptation to changes in dynamics in high noise settings, which are common in robotics appli…
Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic methods have been proposed to tackle different MOCO problems over the past decades. In this work, we generalize the idea of neural combinatorial optimization, and develop a learning-based approach to approximate the whole Pareto set for a given MOCO problem without further search procedure. We propose a single preference-conditioned model to directly generate appr…
