An Improved Ideal Point Setting in Multiobjective Evolutionary Algorithm Based on Decomposition

MOEA/D decomposes a multi-objective optimization problem into a number of single objective optimization problems. Each single objective optimization problem is defined by a scalarizing function using a weight vector. In MOEA/D, there are several scalarizing approaches such as the weighted Tchebycheff, the weighted sum, and the PBI (penalty-based boundary intersection). However, these conventional scalarizing approaches face a difficulty to approximate a widely spread Pareto front in some problems. To enhance the spread of Pareto optimal solutions in the objective space and improve the search performance of MOEA/D especially in many-objective optimization problems, in this work we propose the inverted PBI scalarizing approach which is an extension of the conventional PBI. We use many-objective knapsack problems and WFG4 problems with 2-8 objectives, and compare the search performance of NSGA-III and four MOEA/Ds using the weighted Tchebycheff, the weighted sum, the PBI and the inverted PBI. As results, we show that MOEA/D using the inverted PBI achieves higher search performance than other algorithms in problems with many-objectives and the difficulty to obtain a widely spread Pareto front in the objective space.

A collaborative decomposition-based evolutionary algorithm integrating normal and penalty-based boundary intersection methods for many-objective optimization

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given Pareto front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter-plots. Experiments are presented for three different combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem and multiobjective vehicle routing problem with time windows. Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

New opportunities and challenges arise in power system operations due to the energy transition from fossil fuels to renewable energy resources coupled with the liberalization of electricity markets. These opportunities appear in the form of energy flexibility, and the uncertainty of renewable generation challenges power system security of supply. This paper presents an efficient energy management model that considers available flexibility from active industrial networks connected to the power distribution grid. Installation of storage units in the industrial grid provides flexibility. The goal is to solve a multi-objective optimal power flow problem to reduce system costs and carbon emissions. In the proposed two-fold approach, Tchebycheff's decomposition method breaks down the multi-objective problem into scalar subproblems, which are then singularly minimized using a distributed gradient projection algorithm. Distributed computation helps retain the data privacy of each participant. The algorithm is applied to modified IEEE radial test network to demonstrate achieved cost benefits and carbon footprint reduction.

Multi-objective evolutionary algorithm has two goals i.e. diversity and convergence while solving MOP (Multi Objective Problem). These two goals can be achieved by proper selection of solutions. Real difficulty is selection of solution in presence of multiple conflicting objectives. MOP can be solved either by considering MOP as a whole or by using decomposition methods which solves scalar optimization sub problems simultaneously by evolving a population of solutions. This paper proposes decomposition based multi-objective genetic algorithm with Opposition operation. In this work Opposition Based Learning (OBL) concept is used in a unique way for weight vector generation. Also to have diversity among solutions and proper exploration of search space opposition based learning concept is used for population initialization and both parent and opposite parent are allowed to reproduce. The performance of the proposed methods is investigated on problems of CEC09 test suit. The experiments conducted show that OBL improves the performance of decomposition based Multi-objective Genetic Algorithm (DMOGA).

A modified PBI approach for multi-objective optimization with complex Pareto fronts

It is difficult to maintain the balance between convergence and diversity for many-objective optimization problems (MaOPs) in the algorithms of evolutionary multi-objective (EMO). EMO algorithms are useful technology to solve the multi-objective optimization problems (MOPs). However, with the larger of optimization objectives, enough Pareto selection pressure will be loosed, and results in the performance of the algorithms are significantly reduced. The decomposition-based EMO developed for MaOPs have been shown to be effective, and the BBO algorithm is a low-complexity algorithm. In this paper, a hybrid decomposition-based BBO/Complex algorithm (HDB/BBO) for MaOPs is proposed. First, a set of uniformly distributed weight vectors and K-means aggregate method is introduced for decomposing MaOPs into several subsystems. Then, inferior migrated islands will not be chosen unless they pass the Metropolis criterion twice during the within-subsystem migration and cross-subsystem migration. The penalty-based boundary intersection (PBI) distance to calculate neighbor islands distance for balancing the algorithm of convergence and diversity. Finally, after mutation and clear duplication, a uniform distribution Pareto set can be obtained. Experimental results on both DTLZ and WFG benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.

Simultaneous optimization of two or more objectives is an instance of multi-objective optimization (MOO). However, for most of the Multi-Objective Problems (MOPs), no single solution can optimize all the objective functions simultaneously. Evolutionary algorithms are a type of optimization algorithm used for constructing a well-distributed optimal front more quickly than a much more efficient approach. One of the most commonly used algorithms in this regard is differential evolution (DE). To solve the problem of non-dominated sorting for Multi-Objective DE (MODE), an approach is proposed that reduces the time complexity. DE is commonly recognized as one of the best methods for solving the MOPs. Several versions of DEs have been proposed for MOPs. This article proposes a novel mutation technique, named Environmental Parameter-based Multi-Objective Differential Evolution (EP-MODE) that acquires two additional environmental parameters to preserve diversity and accelerate the convergence. The proposed approach also reduces the time complexity of non-dominated sorting for Multi-Objective DE (MODE). The proposed mutation's performance has been evaluated on DTLZ series and ZDT series benchmark test functions on the Pareto-optimal front and compared with existing multi-objective algorithms (MODE and MODE-RMO). The solution comparatively verifies that the proposed EP-MODE outperforms most of the MODEs for lower dimension functions and higher functions. HIGHLIGHTS New environmental parameters-based mutation has been introduced in a differential evolution algorithm to solve multi-objective optimization problems (EP-mode) The addition of two additional environmental parameters to EP-mode has been found to be appropriate for maintaining diversity while also accelerating the convergence rate EP-MODE evaluated on bi-objective (DTLZ series) and tri-objective (ZDT series) benchmark test functions on the Pareto-optimal front and found EP-MODE's efficiency is higher than that of the MODE algorithm and the MODE algorithm with a ranking-based mutation operator GRAPHICAL ABSTRACT

Adaptive genetic algorithms applied to dynamic multiobjective problems

Computer‐Aided Optimization of Surveillance Cameras Placement on Construction Sites

The bilevel optimisation problem (BLP) is a subclass of optimisation problems in which one of the constraints of an optimisation problem is another optimisation problem. BLP is widely used to model hierarchical decision making where the leader and the follower correspond to the upper level and lower level optimisation problem, respectively. In BLP, the optimal solutions to the lower level optimisation problem are the feasible solutions to the upper level problem, which makes it particularly difficult to solve. This paper proposes a novel hardware architecture known as Recursive Pipelined Genetic Propagation (RPGP), to solve BLP efficiently on FPGA. RPGP features a graph of genetic operation nodes which can be scaled to exploit hardware resources. In addition, the topology of the RPGP graph can be changed at run-time to escape from local optima. We evaluate the proposed architecture on an Altera Stratix-V FPGA, using a benchmark bilevel optimisation problem set. Our experimental results show that RPGP can achieve a significant speed-up against previous work.

This paper proposes a modified particle swarm optimization algorithm for engineering optimization problems with constraints, in which the penalty function is employed to the traditional PSO algorithm, and at the same time adjusts the personal optimum and global optimum to make PSO being able to solve the non-linear programming problems, then the multi-objective problem can be converted into single objective problem. Moreover, the constraint term played its role in the process of generating particles, those pariticles which don't meet the constraint condition are eliminated. The actual engineering design optimization problem is tested and the results show that the multi-objective particle swarm optimization algorithm can be used to solve the multi-objective constrained optimization problem. Comparison with Genetic Algorithm confirms that the proposed algorithm can find better solutions, and converge quickly.

In Multiobjective Optimization problems the objective functions may have different scales, which leads to a neglecting of one or more objective functions. The most common-used way in the literature to solve this drawback is to normalize the objective space; however, a set of uniformly distributed solutions in the normalized objective space may not be uniformly distributed in the original objective space with more than two objective functions. In this work, we present an improved version of the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) which incorporates a new aggregation technique based on the Normal Boundary Intersection approach and the Tchebycheff approach (MOEA/D-NBI) for solving 3-objective optimization problems with different scales of objectives.

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

A global optimization method for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the global topology optimization method in flow problems, this research works on two single-objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and the multi-objective optimization problem, which combines these two problems. The shape of flow channels is represented by the level set function, and the pressure loss and the temperature of the channels are evaluated by the Building-Cube Method (BCM), which is a Cartesian-mesh CFD approach. The proposed method resulted in an agreement with previous study in the single-objective problems in its topology, and achieved global exploration of non-dominated solutions in the multi-objective problem.