Evolutionary Large-Scale Multi-Objective Optimization: A Survey

Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

A study of uncertain multi-objective nonlinear programming problems for rough intervals

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

AIEADA 1.0: Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior, and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by four orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIAEDA (Artificial Intelligence Emulator Assisted Data Assimilation).

Optimal Charging Management of Microgrid-Integrated Electric Vehicles

The relevance of electric vehicles (EVs) is increasing along with the relative issues. The definition of smart policies for scheduling the EVs charging process represents one of the most important problems. A discrete-event approach is proposed for the optimal scheduling of EVs in microgrids. This choice is due to the necessity of limiting the number of the decision variables, which rapidly grows when a small-time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles in a microgrid characterized by renewable energy source, a storage element, the connection to the main grid, and a charging station. The objective function to be minimized results from the weighted sum of the cost for purchasing energy from the external grid, the weighted tardiness of the services provided, and a cost related to the occupancy of the socket. The approach is tested on a real case study.

A modular framework for optimal scheduling of industrial processes

This paper proposes an extended Petri net formalism as a suitable language for composing optimal scheduling problems of industrial production processes with real and binary decision variables. The proposed approach is modular and scalable, as the overall process dynamics and constraints can be collected by parsing of all atomic elements of the net graph. To conclude, we demonstrate the use of this framework for modeling the moulding sand preparation process of a real foundry plant.

Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

A Short Inroad to Optimized Compactification of Composite Neutronic Shields

Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are known to be optimized multilayered composites. This paper is a simplified short inroad to the complex problem of optimizing the design of such shields when they attenuate a neutron beam to extremise certain quality criteria, in plane geometry, subject to equality and inequality constraints. In the equality constraints, the interfacial polychromatic neutron fluxes are solutions to course-mesh finite-difference holonomic state equations. The set of these interfacial fluxes act as state variables,while the set of layer thicknesses, or their poisoning (by added neutron absorbers) concentrations are decision variables. The entire procedure is then demonstrated to be reducible to standard Kuhn-Tucker semi-linear programming that may also lead robustly to an optimal sequence for these layers.

Three-Parameter Regulation Rules for the Long-Term Optimal Scheduling of Multiyear Regulating Storage Reservoirs

The perennial storage water level (PL), the water level at the end of wet season (WL), and the water level at the end of dry season (DL) are three critical water levels for multiyear regulating storage (MRS) reservoirs. Nevertheless, the three critical water levels have not been paid enough attention, and there is no general method that calculates them in light of developing regulating rules for MRS reservoirs. In order to address the issue, three-parameter regulation (TPR) rules based on the coordination between the intra- and interannual regulation effects of MRS reservoirs are presented. Specifically, a long-term optimal scheduling (LTOS) model is built for maximizing the multiyear average hydropower output (MAHO) of a multireservoir system. The TPR rules are a linear form of rule with three regulation parameters (annual, storage, and release regulation parameters), and use the cuckoo search (CS) algorithm to solve the LTOS model with three regulation parameters as the decision variables. The approach of utilizing the CS algorithm to solve the LTOS model with the WL and DL as the decision variables is abbreviated as the OPT approach. Moreover, the multiple linear regression (MLR) rules and the artificial neural network (ANN) rules are derived from the OPT approach-based water-level processes. The multireservoir system at the upstream of Yellow River (UYR) with two MRS reservoirs, Longyangxia (Long) and Liujiaxia (Liu) reservoirs, is taken as a case study, where the TPR rules are compared with the OPT approach, the MLR rules, and the ANN rules. The results show that for the UYR multireservoir system, (1) the TPR rules-based MAHO is about 0.3% (0.93 × 108 kW∙h) more than the OPT approach-based MAHO under the historical inflow condition, and the elapsed time of the TPR rules is only half of that of the OPT approach; (2) the TPR rules-based MAHO is about 0.79 × 108 kW∙h more than the MLR/ANN rules-based MAHO under the historical inflow condition, and the TPR rules can realize 0.1–0.4% MAHO more than the MLR and ANN rules when the reservoir inflow increases or reduces by 10%. According to the annual regulation parameter, the PLs of Long and Liu reservoirs are 2572.3 m and 1695.2 m, respectively. Therefore, the TPR rules are an easy-to-obtain and adaptable LTOS rule, which could reasonably and efficiently to determine the three critical water levels for MRS reservoirs.

Optimizing Customized Transit Service considering Stochastic Bus Arrival Time

The introduction of customized bus (CB) service intends to expand and elevate existing transit service, which offers an efficient and sustainable alternative to serve commuters. A probabilistic model is proposed to optimize CB service with mixed vehicle sizes in an urban setting considering stochastic bus arrival time and spatiotemporal demand, which minimizes total cost subject to bus capacity and time window constraints. The studied optimization problem is combinatorial with many decision variables including vehicle assignment, bus routes, timetables, and fleet size. A heuristic algorithm is developed, which integrates a hybrid genetic algorithm (HGA) and adaptive destroy-and-repair (ADAR) method. The efficiency of HGA-ADAR is demonstrated through numerical comparisons to the solutions obtained by LINGO and HGA. Numerical instances are carried out, and the results suggested that the probabilistic model considering stochastic bus arrival time is valuable and can dramatically reduce the total cost and early and late arrival penalties. A case study is conducted in which the proposed model is applied to optimize a real-world CB service in Xi’an, China. The relationship between decision variables and model parameters is explored. The impacts of time window and variance of bus arrival time, which significantly affect service reliability, are analysed.

An improved weighted optimization approach for large-scale global optimization

It is a great challenge for ordinary evolutionary algorithms (EAs) to tackle large-scale global optimization (LSGO) problems which involve over hundreds or thousands of decision variables. In this paper, we propose an improved weighted optimization approach (LSWOA) for helping solve LSGO problems. Thanks to the dimensionality reduction of weighted optimization, LSWOA can optimize transformed problems quickly and share the optimal weights with the population, thereby accelerating the overall convergence. First, we concentrate on the theoretical investigation of weighted optimization. A series of theoretical analyses are provided to illustrate the search behavior of weighted optimization, and the equivalent form of the transformed problem is presented to show the relationship between the original problem and the transformed one. Then the factors that affect problem transformation and how they take affect are figured out. Finally, based on our theoretical investigation, we modify the way of utilizing weighted optimization in LSGO. A weight-sharing strategy and a candidate solution inheriting strategy are designed, along with a better allocation of computational resources. These modifications help take full advantage of weighted optimization and save computational resources. The extensive experimental results on CEC’2010 and CEC’2013 verify the effectiveness and scalability of the proposed LSWOA.